Assaf Rinot (Bar-Ilan University)

The small Dowker space problem

It is well-known that the product of two normal topological spaces need not be normal, but what about the normality of the product of a normal space $X$ with the unit interval $[0,1]$? A counterexample space $X$ is called a "Dowker space". In 1972, Rudin proved that such a space exists, but it remains open whether there must exist a Dowker space of size $\aleph_1$. In this talk, we shall report on a joint work with Shalev and Todorcevic in which we present a weak sufficient condition for the existence of a small Dowker space.

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