nLab
countably tight 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

Idea

The topology of a countably tight space is determined by countable subsets similar to how in a sequential space the topology is generated by sequences.

Definition

A topological space XX is called countably tight or countably generated if a set AXA \subset X is closed if (and hence only if) for each countable subset DXD \subset X the intersection ADA \cap D is closed in the relative topology on DD.

Categorical properties

The category of countably tight spaces is a coreflective subcategory of Top. More precisely, it is the coreflective hull of the subcategory of countable spaces.

Properties

Implications

References

Last revised on April 5, 2019 at 19:38:50. See the history of this page for a list of all contributions to it.