# Contents

## Definition

A topological space is called fully normal if every open cover $\{U_i \subset X\}_{i \in I}$ has a refinement by an open cover $\{V_j \subset X\}_{j \in J}$ such that every star in the latter cover is contained in a patch of the former.

Here for $x \in X$ a point, then the star of $x$ is the union of the patches that contain $x$:

$star(x,\mathcal{V}) \;\coloneqq\; \left\{ V_j \in \mathcal{V} \;\vert\; x \in V_J \right\}$

## Properties

Last revised on May 23, 2017 at 15:06:19. See the history of this page for a list of all contributions to it.