DMS Graduate Student Seminar

Speaker: Dr. Ziqin Feng

Title: ZFC, Posets, and Metrization

Abstract: I will briefly introduce one of the foundations of modern mathematics, Zermelo-Fraenkel set theory, i.e., ZFC. Then I will discuss one of recent metrization results in topology which is independent of ZFC.  In fact, we show that when \(\omega_1<\mathfrak{b}\), a compact space is metrizable if the local base at each point is a Tukey quotient of the collection of compacts sets in a Polish space. The result doesn't hold when \(\omega_1=\mathfrak{b}\). This answers a recently-published open question.