nLab
cellular map

Contents

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

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Idea

A continuous function between topological spaces which respects a given cell complex-structure on these spaces is called a cellular map.

Definition

Let XX and YY be CW-complexes and let X nX_n (respectively Y nY_n ) denote the nn-skeleton of XX (respectively YY). Then a continuous function f:XYf:X \rightarrow Y is said to be cellular if it takes nn-skeletons to nn-skeletons for all n=0,1,2,...,n = 0,1,2,..., i.e, if

f(X n)Y n f(X_n ) \subseteq Y_n

for all natural numbers nn.

Last revised on December 18, 2019 at 08:35:24. See the history of this page for a list of all contributions to it.