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.”

“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.”

“The purpose of this paper is to construct (without using any set theoretic conditions beyond the axiom of choice) a normal Hausforff space X whose Cartesian product with the closed unit interval I 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 ...”

“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.”