# Mary Ellen Rudin

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**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.

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## Quotes[edit]

- 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.
- (1969). "Souslin's Conjecture".
*The American Mathematical Monthly***76**(10): 1113–1119. DOI:10.1080/00029890.1969.12000425.

- (1969). "Souslin's Conjecture".

- 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.***73**: 179–186. DOI:10.4064/fm-73-2-179-186.

- (1971)"A normal space

- 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.*Lectures on Set Theoretic Topology*. 31 December 1975. p. 3. ISBN 9780821816738.

- A space has the shrinking property if, for every open cover {V
_{a}| a ∈ A}, there is an open cover {W_{a}| 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.- (1983). "The Shrinking Property".
*Canadian Mathematical Bulletin***26**(4): 385–388. DOI:10.4153/CMB-1983-064-x.

- (1983). "The Shrinking Property".

## Quotes about Mary Ellen Rudin[edit]

- 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. (1 June 2015), "Memories of Mary Ellen Rudin",
*Notices of the American Mathematical Society***62**(6): 617–629, doi: (quote from p. 620)

- István Juhász, as quoted in Benkart, Georgia; Džamonja, Mirna; Roitman, Judith, eds. (1 June 2015), "Memories of Mary Ellen Rudin",