# Cellular Approximation Theorem

### (Theory)

Tech

###### Theory ## What is Cellular approximation theorem?

In algebraic topology, in the cellular approximation theorem, a map between CW-complexes can always be taken to be of a specific type. Concretely, if X and Y are CW-complexes, and f : X → Y is a continuous map, then f is said to be cellular, if f takes the n-skeleton of X to the n-skeleton of Y for all n, i.e. if for all n. The content of the cellular approximation theorem is then that any continuous map f : X → Y between CW-complexes X and Y is homotopic to a cellular map, and if f is already cellular on a subcomplex A of X, then we can furthermore choose the homotopy to be stationary on A. From an algebraic topological viewpoint, any map between CW-complexes can thus be taken to be cellular.

### Technology Types

propositionstatementtheoremtheorems in algebraic topologytheory

### Synonyms

Cellular approximationCellular map

## Tech Info

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— Date merged: 11/6/2021, 1:32:53 PM
— Date scraped: 5/20/2021, 6:20:39 PM