Reconstructing compact metrizable spaces

Compact Monotonically Metacompact Spaces Are Metrizable

Monotonically metacompact spaces were recently introduced as an extension of the concept of monotonically compact spaces. In this note we answer a question of Popvassilev, and Bennett, Hart, and Lutzer, by showing that every compact, Hausdorff, monotonically (countably) metacompact space is metrizable. We also show that certain countable spaces fail to be monotonically (countably) metacompact.

Compact Metrizable Groups Are Isometry Groups of Compact Metric Spaces

This note is devoted to proving the following result: given a compact metrizable group G, there is a compact metric space K such that G is isomorphic (as a topological group) to the isometry group of K.

Countable Compact Hausdorff Spaces Need Not Be Metrizable in Zf

We show that the existence of a countable, first countable, zerodimensional, compact Hausdorff space which is not second countable, hence not metrizable, is consistent with ZF. 1. Notation and terminology Definition 1.1. Let (X,T ) be a topological space and B a base for T . (i) X is said to be compact if every open cover U of X has a finite subcover V . X is said to be compact with respect to ...

- Metrizable Spaces and Their Applications

In this paper we introduce and study so-called k∗-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By definition, a Hausdorff topological space X is k∗-metrizable if X is the image of a metrizable space M under a continuous map f : M → X having a section s : X → M ...

Proto-metrizable fuzzy topological spaces