Sibe Mardesic 1927-2016 distinguished Croatian mathematician and Fellow of the AMS

http://www.croatia.org/crown/articles/10852/1/Sibe-Mardesic-1927-2016-distinguished-Croatian-mathematician-and-Fellow-of-the-AMS.html

By Nenad N. Bach and Darko Žubrinić

Published on 06/18/2016

Professor Sibe Mardešić, University of Zagreb, Croatia, and Professor James Keesling, University of Florida, Gainsville USA,

at a Topology Conference in Bedlewo, Poland, July 7, 2005.

Mathematics geneaology of Sibe Mardešić

Topological Seminar in Zagreb, 1999:

Professors Zvonko Čerin, Krešo Horvatić, Leonhard Rubin (University of Oklahoma, USA), Sibe Mardešić, Vera Tonić (University of Rijeka), Sonja Štimac,

Ivan Ivanšić, Šime Ungar and Nikola Koceić Bilan (University of Split, many thanks for the photo).

In Osijek, Croatia 2008, at the 4th Croatian Mathematical Congress:

professor Mladen Bestvina on the right, on the left academician Sibe Mardešić, distinguished Croatian topologist.

Next to him Ivan Mirković, Croatian-American mathematician, professor at the University of Massachusetts, Amherst, MA., USA.

Both Mladen Bestvina and Ivan Mirković were students of Sibe Mardešić at the University of Zagreb.

Sibe Mardešić: Shape Theory [PDF], Proceedings of the International Congress of Mathematicians, Helsinki 1978

Professor Mardešić had the honor of participating at that Congress as invited lecturer in Section of Topology.

Sibe Mardešić and Jack Segal: Shape Theory

Springer Monographs in Mathematics, 2000

Celebration of the 80th anniversary of Professor Ivan Ivanšić in 2011, a close collaborator of Professor Sibe Mardešić,

organized at the Faculty of Electrical Engineering and Computing

of the University of Zagreb

ShX=ShYâşIââXâIââX

Professors Dragutin Svrtan, University of Zagreb, and Damir Vukičević, University of Split, with academician Sibe Mardešić,

distinguished Croatian topologist, who celebrated hisÂ 85th brithday in 2012 during the 5th Croatian Mathematical Congress in the city of Rijeka.

Sibe Mardešić kao gost Matematičkog kolokvija u Osijeku godine 2006.

Akademik Sibe Mardešić i akademik Zvonimir Janko 2009. g. na FER-u, tijekom proslave

90. obljetnice Zavoda za primijenjenu matematiku.

Sibe Mardešić:*How I Became and Remained a Mathematician / Mathematical Autobiography* (in Croatian), Zagreb 2016,

approx. 480 pp., with numerous photos, ISBN 978-953-169-347-9 2 (published posthumously)

**Pavao Mardešić** (Komiža 1895. - Split 1978.), father of Sibe Mardešić [PDF]

Igor Belamarić:*Životni puti inženjera Pave Mardešića* (2. izd), Split 2015., ISBN 978-953-263-294-1

Find a nonconstant uniformly continuous function*f* : (0,1) -> **R** such that for every rational number

q in (0,1) there is an open interval I_*q* containing *q*, on which *f* is constant.

The first monograph about William Feller, distinguished Croatian-American Mathematician, published in Zagreb 2011.

The author owes his deep gratitude to Professor Mardešić for his kind help during the preparation of the book.

S. Mardesic used to know William Feller in person already since 1956, when William Feller visited his native city of Zagreb.

William Feller helped Sibe Mardesic, at that time a young scientist in Zagreb, to spend the academic years 1957/58 and 1958/59

at the Institute for Advanced Study in Princeton, see [here]. S. Mardesic was introduced to Feller in person by Professor Zeljko Markovic in his office,

when Feller visited Department of Mathematics and had a lecture there, PMF, Zagreb, in 1956.

According to [Vranic, p. 352], "...not only that Vilim Feller did not hide his Croatian descent, but he was also proud of it."

| Professor Sibe Mardešić: "I have been very devoted and faithful to Mathematics in Zagreb. I dedicated approximately equal shares of my time and energy to research, teaching and organization. I tried to transfer to Zagreb good things that I saw at other more developed places. I paid particular attention to teaching at the graduate level." Professor Sibe Mardešić is a member of the Croatian Academy of Sciences and a Fellow of the prestigious American Mathemacial Society. He had over 260 lectures at conferences and universities in 20 countries. Besides his native Croatian, he fluently spoke six languages. We provide an interesting interview with him conducted by Professor James Keesling, USA. |

Member of Croatian Academy of Sciences and Arts and a Fellow of the American Mathematical Society

Professor Sibe Mardešić, distinguished international expert in the field of General and Algebraic Topology. Photo by Željko Vojković.

Â AN INTERVIEW WITH SIBE MARDESIC James Keesling, University of Florida, USASibe Mardesic is a mathematician who has had a considerable influence on research in topology in the course of his career. It is my pleasure not only to know his mathematics, but also to know him personally. His manner is just as attractive as his mathematics. He is personable, gracious and unassuming. We have a joint paper together and he is the ideal collaborator. His clear mathematical mind and congenial manner made working together a very gratifying experience for me. When we began our work he had a clear idea what results could be expected and what tools would be useful. He also knew that the devil was in the details and was never satisfied until every step of each proof was absolutely clear. Sibe has attained preeminent stature, but that was not the sort of thing that he set his sights on. His focus was always on mathematics itself and the beauty he saw in it. As he says in our interview, At the end of the interview there is a biographical sketch which includes Sibe's major accomplishments and some of the recognition that he has been accorded. Please do not think that this is the final chapter in the life of Sibe Mardesic. He is still active and there is more to come.
The family on both, my father's side (Mardesic) and my mother's side (Karaman), is from Dalmatia, the coastal region of Croatia. Presence of the Mardesices in Komiza on the island is documented since 1539. They fished sardine and cultivated grapevine. My grandfather Sibe spent 30 years as lighthouse keeper on remote islands of the Adriatic. My father Pavao was a naval architect and a mechanical engineer. My mother Anka comes from a family of merchants from the coast town of Split and its hinterland.
My father studied at the well-known Technical University in Vienna. The period from 1923 to 1929 my parents spent in Hamburg, where I was born on June 20, 1927 in Bergedorf, a suburb of Hamburg. In 1929 we moved to Chile, where my father worked in a factory near Antofagasta. We returned to Split in 1930 and this concludes my childhood traveling. My parents, beside their mother tongue Croatian, spoke fluently Italian, German, French, English and Spanish. This gave me a good start and enabled me to get pretty good in these languages and Russian.
My father wanted me to become an engineer and paid particular attention to my school grades in mathematics. Towards the end of the Second World War I joined the Yugoslav Navy, where I worked in the Meteorology Service. There I met a student of mathematics of the University of Zagreb, Mr. B. Makjanic, who later became a known meteorologist. He introduced me to mathematics beyond the school level. I was fascinated by what he told me about sets and their cardinal numbers and I made the decision to study mathematics as soon as I got released from the Navy.
I enrolled at the University of Zagreb in 1946/47. At that time there were few professors at the Mathematics Department. I was attracted to set theory by Prof. Dj. Kurepa and to geometry by Prof. R. Cesarec.
Shortly after obtaining my B.Sci. in 1950, I became assistant to Prof. Zeljko Markovic. In his youth he spent a year in Paris and was fascinated by the work of H. PoincarĂŠin celestial mechanics. He wanted me to become interested in dynamical systems, and it was clear to him that to do global analysis one needs a good understanding of topology. Therefore, he suggested that I first study "Lehrbuch der Topologie" by H. Seifert and W. Threlfall. This turned out to be very good advice. I read the book in great detail and fell in love with (algebraic) topology. In my Ph. D. thesis I considered some problems of K. Borsuk concerning homology of function spaces. In the process of writing the thesis I corresponded with S. Lefschetz, who at some point suggested that I visit the Institute for Advanced Study in Princeton. With letters of recommendation by Borsuk, Eilenberg and Kuratowski, I was accepted to the Institute, where I spent the years 1957/58 and 1958/59. In Princeton I attended lectures by R. H. Fox, J. Milnor, J. Moore, N. Steenrod and G. Whitehead and I became a topologist.
It was most fortunate for me that I met Vera. This happened in 1948/49, when I was a junior and she was a freshman. Throughout my life I always had her full support. She understood how important my work was to me and she provided a happy and secure environment for me. The fact that she is herself a mathematician enabled her to follow my work and accompany me on many of my mathematical trips. She did most of her work under the guidance of Prof. Victor Klee.
My son Pavao is indeed a mathematician. He has a B. Sci. and a M. Sci. from Zagreb and a Ph. D. from UniversitĂŠde Bourgogne, Dijon, France, where he now has a position. His area is dynamical systems, in particular, singularities of polynomial vector fields in the plane. My daughter Milica has a Ph. D. in linguistics from Zagreb. We have five grandchildren, from 10 to 3 years old, which give us a lot of joy and pleasure.
It appears that my most successful result is the factorization theorem in dimension theory, which is quoted in most books on dimension theory. I like my work on continuous images of ordered continua. I believe that I will be remembered for my contributions to shape theory and strong homology. My shape theory book with Jack Segal has been well received. I have a new book on strong shape and Steenrod homology which is in preparation. I am hoping that it will be received as well as the shape theory book has. I also like my work with L. Rubin and T. Watanabe on approximate inverse systems. I always wanted to be an algebraic topologist, but did not quite succeed. Therefore, I like my recent results concerning higher derived limits of homological progroups.
I have been very devoted and faithful to Mathematics in Zagreb. I dedicated approximately equal shares of my time and energy to research, teaching and organization. I tried to transfer to Zagreb good things that I saw at other more developed places. I paid particular attention to teaching at the graduate level.
I first try to understand the material properly. Then I try to present it clearly, giving the necessary background. Enthusiasm of the teacher and an honest, respectful and friendly approach to students are essential features of successful teaching.
I never thought very much about the direction in which I was going. Some questions would just attract my imagination and I would follow that trail persistently and for an extended period of time. The internal beauty and consistency of a result is what always mattered to me.
I was deeply shaken by these events. Fortunately, unlike many others, my own family was spared from personal tragedies. I hope that the situation in my country will gradually stabilize. It is now important that we resume the excellent ties which we had before with our colleagues abroad. Let us be in touch through mail, visits and common programs. It would be nice if we could together revive the Dubrovnik topology meetings. I wonder if there would be a way to help us fill up the gaps in our library which occurred during the war.
## Sibe Mardesic - Biography
Elementary and high school in Split (Croatia). B. Sci. in Mathematics 1950 (Faculty of Natural Sciences and Mathematics, Zagreb), Ph. D. in Mathematical Sciences 1957 (University of Zagreb). Ph. D. Thesis: Sibe Mardešić is a member of Academia Europaea (The Academy of Europe)
Faculty of Natural Sciences and Mathematics, Zagreb: Asst. 1951, Asst. Prof. 1960, Associate Professor 1962, Professor 1966. Retired 1991. Chairman of the Mathematics Department, Faculty of Natural Sciences and Mathematics, Zagreb, 1961/62; Vicedean, Faculty of Natural Sciences and Mathematics, Zagreb, 1964/65; President of the Council of Faculty of Natural Sciences and Mathematics, Zagreb, 1966/67; Dean of Faculty of Natural Sciences and Mathematics, Zagreb 1974/75 and 1975/76; Dean of the Mathematics Department of Faculty of Natural Sciences and Mathematics, Zagreb 1983/84; Head of the Chair for Topology of the Mathematics Department of Faculty of Natural Sciences and Mathematics, Zagreb, from 1978 to 1982. Head of the Graduate School for Mathematics of the University of Zagreb from 1960 to 1971; Editor in chief of the journal
Visiting Member of the Institute for Advanced Study, Princeton, N.J., 1957/58 and 1958/59; Visiting Lecturer, University of Washington, Seattle 1965/66. Visiting Professor, University of Heidelberg, 1971/72; Visiting Professor, University of Pittsburgh, Fall Semester 1972/73; Visiting Professor, University of Utah, Salt Lake City, Fall Semester 1977/78; Visiting Professor, University of Kentucky, Lexington, Spring Semester 1977/78; Visiting Professor, University of Washington, Seattle, Spring Semester 1987/88 and Fall semester 1988/89; Research programs and series of lectures in the duration of one month approximately at the following universities: L'Aquila (1979), Tsukuba (1981), Perugia (1985 and 1990), Oklahoma (1987), Milano (1993).
Areas of primary interest: Topology, in particular, inverse systems, dimension theory, shape theory and homology theory. 124 published research papers, 19 professional papers and 3 books. Papers published in various journals including: Topology and its Applications, Topology, Fundamenta Mathematicae, Transactions of the American Mathematical Society, Proceedings of the American Mathematical Society, Bulletin of the American Mathematical Society, Comptes Rendus de l'Academie Paris, Doklady Akademii Nauk SSSR, Michigan Mathematical Journal, Illinois Mathematical Journal, Pacific Mathematical Journal, Rocky Mountains Mathematical Journal, Bulletin of the Polish Academy of Sciences, Uspehi Matemativ ceskih Nauk, Tsukuba Journal of Mathematics, Mathematica Japonica.
Almost 500 reviews for international reviewing journals (Mathematical reviews and Zentralblatt fĂźr Mathematik). Over 260 lectures at conferences and universities in 20 countries. Undergraduate courses in Mathematical Analysis and Topology. 13 different Graduate courses in Topology.
Associated Member of the Yugoslav (Croatian) Academy of Sciences and Arts 1975; Member of the Yugoslav (Croatian) Academy of Sciences and Arts JAZU (HAZU) 1988; Member of Academia Europaea 1990. Member of the American Mathematical Society since 1958; Member emeritus of the American Mathematical Society since 1992. Professor emeritus of the University of Zagreb, 1996. Award for Scientific achievements of the Republic of Croatia Interview from Volume 1, #3 of TopCom Source at.yorku.ca; published in 1996. Many thanks to Professor James Keesling for his kind permission to publish his interview for the readers of the CROWN. D.Ž. The interview has been translated into Croatian by Dr. Željko Hanjš, University of Zagreb: James Keesling: Intervju s akademikom Sibom Mardešićem [PDF], Matematičko-fizički list, Zagreb, 2008.-2009., str. 156-158.Many thanks to Branimir Dakić, prof., Zagreb, for kind permission to reproduce some of the photos from his article [PDF] published in Matematika i škola no. 41, 2007. |

Professor Sibe Mardešić, University of Zagreb, Croatia, and Professor James Keesling, University of Florida, Gainsville USA,

at a Topology Conference in Bedlewo, Poland, July 7, 2005.

Mathematics geneaology of Sibe Mardešić

Sibe Mardešić: Kako sam postao i ostao matematičar (60 min.), Zagreb 2011.

Topological Seminar in Zagreb, 1999:

Professors Zvonko Čerin, Krešo Horvatić, Leonhard Rubin (University of Oklahoma, USA), Sibe Mardešić, Vera Tonić (University of Rijeka), Sonja Štimac,

Ivan Ivanšić, Šime Ungar and Nikola Koceić Bilan (University of Split, many thanks for the photo).

In Osijek, Croatia 2008, at the 4th Croatian Mathematical Congress:

professor Mladen Bestvina on the right, on the left academician Sibe Mardešić, distinguished Croatian topologist.

Next to him Ivan Mirković, Croatian-American mathematician, professor at the University of Massachusetts, Amherst, MA., USA.

Both Mladen Bestvina and Ivan Mirković were students of Sibe Mardešić at the University of Zagreb.

Sibe Mardešić: Shape Theory [PDF], Proceedings of the International Congress of Mathematicians, Helsinki 1978

Professor Mardešić had the honor of participating at that Congress as invited lecturer in Section of Topology.

Sibe Mardešić and Jack Segal: Shape Theory

Springer Monographs in Mathematics, 2000

Celebration of the 80th anniversary of Professor Ivan Ivanšić in 2011, a close collaborator of Professor Sibe Mardešić,

organized at the Faculty of Electrical Engineering and Computing

of the University of Zagreb

Akademik Sibe Mardešić, međunarodno poznati hrvatski topolog, u polsatnom predavanju opisao je

glavne matematičke rezultate dugogodišnjih istraživanja profesora Ivana Ivanšića.

Akademik Sibe Mardešić, [MP3], 35 min., opisao je znanstveni rad profesora Ivana Ivanšića u pet područja:

- PL-topologija (
**p**o dijelovima**l**inearna topologija,**p**iecewise**l**inear topology) - Teorija oblika
- Slabi fibranti
- Teorija proširenja
- Univerzalni prostori

Akademik Sibe Mardešić opisuje Ivanšićev teorem o komplementima iz teorije oblika:

Akademik Sibe Mardešić: Radovi profesora Ivanšića u području topologije spadaju među najvažnije koje je dala ova sredina.

U prvom redu profesori Nikica Uglešić, Sibe Mardešić i Vesna Županović, u trećem profesori Mirko Primc i Hrvoje Kraljević.

Akademik Sibe Mardešić sa suprugom Verom u društvu sa svojim nekadašnjim studentima,

profesorima Vesnom Županović i Nikicom Uglešićem u Crnoj vijećnici FER-a.

Akademik Sibe Mardešić: *Životni put akademika Vladimira DevidĂŠa* (1925.-2010.) [MP3], 2011., predavanje održano u Hrvatskoj akademiji znanosti i umjetnosti

Sibe Mardešić: Vode i more otoka Visa; 2012.

Sibe Mardešić reporting about his current research at the Geometric Topology II Conference in Dubrovnik, 2002

Professors Dragutin Svrtan, University of Zagreb, and Damir Vukičević, University of Split, with academician Sibe Mardešić,

distinguished Croatian topologist, who celebrated hisÂ 85th brithday in 2012 during the 5th Croatian Mathematical Congress in the city of Rijeka.

Sibe Mardešić kao gost Matematičkog kolokvija u Osijeku godine 2006.

Akademik Sibe Mardešić i akademik Zvonimir Janko 2009. g. na FER-u, tijekom proslave

90. obljetnice Zavoda za primijenjenu matematiku.

Akademik Sibe Mardešić, akademik Zvonimir Janko, prof.dr.sc. Vladimir Ćepulić

Prof.dr.sc. Juraj Šiftar i akademik Sibe Mardešić

Sibe Mardešić:

approx. 480 pp., with numerous photos, ISBN 978-953-169-347-9 2 (published posthumously)

Igor Belamarić:

Najznačajniji izum diplomiranog inženjera brodogradnje i brodskog strojarstva Pave Mardešića (1985., Komiža - 1978., Split) je postupak za gradnju drvenih brodova koji ne propuštaju vodu patentiran 1931. godine i koji se smatra jednim od najvećih doprinosa tehnologiji gradnje drvenog broda u povijesti. Pisac, pak, ove knjige je bio glavni projektant u splitskom brodogradilištu i stoga je razumljivo njegovo zanimanje za Mardešića. Kao što i sam naslov kaže, Belamarić prati Mardešićev životni put. Knjiga je bogato ilustrirana. Izvor. |

Dr. Pina Milišić, Dr. **Pavao Mardešić** (son of Prof. Sibe Mardešić, University of Bourgogne, Dijon, France), Dr. Vesna Županović,

Dr. Domagoj Vlah, Dr. Lana Horvat Dmitrović and Dr. Maja Resman.

Vesna Županović defended her PhD under the guidance of Pavao Mardešić, while

Maja Resman defended her PhD under the guidance Professors Pavao Mardešić and Vesna Županović.

Find a nonconstant uniformly continuous function

q

The author owes his deep gratitude to Professor Mardešić for his kind help during the preparation of the book.

S. Mardesic used to know William Feller in person already since 1956, when William Feller visited his native city of Zagreb.

William Feller helped Sibe Mardesic, at that time a young scientist in Zagreb, to spend the academic years 1957/58 and 1958/59

at the Institute for Advanced Study in Princeton, see [here]. S. Mardesic was introduced to Feller in person by Professor Zeljko Markovic in his office,

when Feller visited Department of Mathematics and had a lecture there, PMF, Zagreb, in 1956.

According to [Vranic, p. 352], "...not only that Vilim Feller did not hide his Croatian descent, but he was also proud of it."

Formated for CROWN by Darko Žubrinić

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