All Questions

Recently I've proven the following theorem Theorem. Let $X$ be a zero-dimensional locally compact Hausdorff space. Then the following are equivalent: Every compactification of $X$ is zero-dimensional....

This is a cross post from MSE. I believe that the following problem have already been considered by some sophisticated topologist. Definition 1. A non-compact Hausdorff topological space $X$ is called ...

Question: Let $X$ be a continuum and $p \in X$. Under what conditions does there exist a compactification $\gamma (X-p)$ with $\gamma (X-p) - (X-p)$ connected and nondegenerate? Throughout, $X$ is a ...

Previously, in this post I've shown the following characterization of spaces with only zero-dimensional compactifications: Theorem. Let $X$ be strongly zero-dimensional and $\beta X\setminus X$ ...

Let $\operatorname{Top}$ be the class of topological spaces. Furthermore, let $\mathcal{U}\subset\operatorname{Top}$ and $\mathcal{V}\subset\operatorname{Top}$ classes satisfying the following ...