nLab
fully normal topological space

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents

Definition

A topological space is called fully normal if every open cover {U iX} iI\{U_i \subset X\}_{i \in I} has a refinement by an open cover {V jX} jJ\{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 xXx \in X a point, then the star of xx is the union of the patches that contain xx:

star(x,𝒱){V j𝒱|xV J} star(x,\mathcal{V}) \;\coloneqq\; \left\{ V_j \in \mathcal{V} \;\vert\; x \in V_J \right\}

Examples

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.