3 problems

Let $X$ and $Y$ be second countable, locally compact, noncompact spaces. Write $X^*=\beta X\setminus X$ and $Y^*=\beta Y\setminus Y$, where $\beta X$ and $\beta Y$ are their Čech–S…

CH–PFA conjecture. Under the Continuum Hypothesis, there are nontrivial homeomorphisms of $X^*$, whereas under different set-theoretic axioms, such as the Proper Forcing Axiom or s…

Independence conjecture. The existence of nontrivial homeomorphisms of $X^*$ is independent of the usual axioms of set theory, namely ZFC, the Zermelo–Fraenkel scheme together with…