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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.

2 votes
1 answer
139 views

Uniquely selecting points from open pairwise disjoint refinements of an open cover

Let $\mathcal U$ be an open cover of some space $X$. Let $\{\mathcal V_\alpha:\alpha<\kappa\}$ enumerate all of its pairwise-disjoint open refinements. When is it possible to define sets $Z_\alpha$ su …
Steven Clontz's user avatar
3 votes

What are the names of the following classes of topological spaces?

For (1), $\omega$ bounded. I'm unaware of names for the other concepts.
Steven Clontz's user avatar
1 vote

Strategic vs. tactical closure

Edit: leaving this up just in case (and for the comments), but I'm pessimistic that the idea is recoverable - see discussion below. As JDH observed, there are topological spaces $X$ for which Player I …
Steven Clontz's user avatar