Zoom Meeting https://pitt.zoom.us/j/91215323315

Meeting ID: 912 1532 3315

Zoom

### Abstract or Additional Information

In these two talks, we will illustrate ways in which techniques from set theory can be used to prove theorems in topology. In the first talk we will apply the technique of elementary submodels (ESMs) to provide a surprisingly short proof of Arhangelskii's celebrated theorem that a T3, Lindelöf space with countable pseudocharacter and countable tightness has cardinality at most that of the continuum. We will then begin a discussion, which we continue into the second talk, about how set-theoretic techniques (both including and in addition to ESMs) can be used to study the situations under which metrizability reflects in topological spaces. In particular, we will prove that if every subspace of size aleph_1 of a countably compact space is metrizable, then the space is metrizable.