Mary Ellen Rudin

Mary Ellen Rudin (née Estill, December 7, 1924 – March 18, 2013) was an American mathematician, specializing in set-theoretic topology. She is noteworthy for, among other things, the first construction of a Dowker space and the first proof of Nikiel's conjecture. Quotes Souslin's conjecture sounds simple. Anyone who understands the meaning of countable and uncountable can "work" on it. It is in fact very tricky. There are standard patterns one builds. There are standard errors in judgement one makes. And there are standard not-quite-counter-examples which almost everyone who looks at the problem happens upon. S. Tennenbaum and others have shown that that it is consistent with the axioms of Zermelo-Fraenkel set theory that Souslin's conjecture be either true or false. 10.1080/00029890.1969.12000425 Souslin's Conjecture 1969 The American Mathematical Monthly 76 10 1113–1119 The purpose of this paper is to construct (without using any set theoretic conditions beyond the axiom of choice) a normal Hausforff space whose Cartesian product with the closed unit interval is not normal. Such a space is often called a Dowker space. The question of the existence of such a space is an old and natural one ... 1971 A normal space X for which X × I is not normal Fundam. Math. Polish Academy of Sciences 73 2 179–186 10.4064/fm-73-2-179-186 0224.54019 http://matwbn.icm.edu.pl/ksiazki/fm/fm73/fm73121.pdf Geometric topology was really the dominant new topological theme in the 1950's and differential topology in the 1960's. Algebraic topology did not take a back seat in either development. But something happened in the 1960's which had profound effect upon the part of topology we are concerned with.... Paul Cohen proved that it is consistent with the usual axioms for set theory that the continuum hypothesis be false.In itself this theorem has few consequence in topology for there is very little one can do with not-CH alone. But the technique of proof, called forcing, has translations into Boolean algebra terms, into partial order terms, into terms which lead to remarkable combinatorial statements which are applicable to a wide variety of topological problems related to abstract spaces. https://books.google.com/books?id=SsKcAwAAQBAJ&pg=PA3 Lectures on Set Theoretic Topology 3 9780821816738 31 December 1975 A space has the shrinking property if, for every open cover {Va | a ∈ A}, there is an open cover {Wa | a ∈ A} with for each a ∈ A. lt is strangely difficult to find an example of a normal space without the shrinking property. It is proved here that any ∑-product of metric spaces has the shrinking property. 10.4153/CMB-1983-064-x The Shrinking Property 1983 Canadian Mathematical Bulletin 26 4 385–388 Quotes about Mary Ellen Rudin Our first meeting in person took place at the IMU Congress in Nice in the summer of 1970. Together with my friend and collaborator András Hajnal we were eager to meet her, and this happened right after she arrived in Nice. Her first sentence to us was “I just proved that there is a Dowker space;” i.e., a normal space whose product with the unit interval is not normal. To appreciate the weight of this sentence, one should know that this meant she solved the most important open problem of general topology of the 1960s. István Juhász, as quoted in Benkart, Georgia; Džamonja, Mirna; Roitman, Judith, eds. Memories of Mary Ellen Rudin Notices of the American Mathematical Society 62 6 617–629 June 2015 10.1090/noti1254 https://www.ams.org/notices/201506/rnoti-p617.pdf free (quote from p. 620) External links Category:1924 births Category:2013 deaths Category:Women academics from the United States Category:Women scientists from the United States Category:Mathematicians from Texas Category:Women mathematicians from the United States