The Set Theory seminar continues on Monday (October 8) with the third part of Marion’s talk on Topological Spaces and Set Theory: Michael Spaces.
Date: October 8
Time: 10:30 a.m. – 11:45 a.m.
Room: MP 210
Title: When is a topological product with the unit interval or with the set of irrational numbers “nice”?
This is a continuation of the previous talk, Moore Spaces and Set Theory. In the previous talk we discussed one instance of the problem: How can you tell from just the topology of a space if that topology is generated by a metric?
In this talk we explore an instance of a related problem: When one knows that a metric generates the topology of a space, then one can derive other properties of the space quite easily. For example, the product of any two metric spaces is a metrizable space, and so has all properties common to all metric spaces. If for one of the factors in a product one did not know or have a metric for the topology, what information about the topology would enable one to show that the product has some property shared by all metric spaces?
This question, where one of the factors is the unit interval or is the set of irrational numbers, has fueled intense research for well over half a century. We will survey some of the remarkable findings that have emerged from the ongoing quest to answer such questions.