nLab
simplicial topological space

Context

Topology

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

see also 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 simplicial topological space is a simplicial object in Top.

Often this is called just a simplicial space , if the context is clear.

A special case is that of simplicial manifolds.

Often one is interested in simplicial topological spaces with extra nice properties. See nice simplicial topological space for more on that.

Applications

As with simplicial objects in general, simplicial spaces may serve to model internal ∞-groupoids in Top. Notably there is a rich theory of simplicial topological groups.

References

A standard textbook reference is chapter 11 of

Revised on November 14, 2013 07:08:29 by Adeel Khan (132.252.63.205)