CW complex

A similar statement does, however, hold for spectra instead of CW complexes.

Each CW complex in the definition above (with its given characteristic map ) is called a tile type.

Any "nice" space such as a manifold or CW complex is semi-locally simply connected.

A CW complex is often constructed by defining its skeleta inductively.

For most purposes, the homotopy category of CW complexes is the appropriate choice.

His definition of CW complexes gave a setting for homotopy theory that became standard.

For cellular chains on CW complexes, it is a straightforward isomorphism.

All topological manifolds and CW complexes are locally simply connected.

Roughly speaking, it is difficult to map such a space continuously into a finite CW complex .

Finding good replacements for CW complexes in the purely algebraic case is a subject of current research.

Let be a CW complex.

The requirements of homotopy theory lead to the use of more general spaces, the CW complexes.

Inductively attaching cells along their spherical boundaries to this space results in an example of a CW complex.

This technical requirement is guaranteed when one assumes that is a regular CW complex over .

Assume that the homotopy category of CW complexes is the underlying category, from now on.

A finite two dimensional CW complex , which is a subdivision of .

If one considers the control flow graph as a 1-dimensional CW complex called , then the fundamental group of will be .

The converse statement also holds: any functor represented by a CW complex satisfies the above two properties.

Let be a regular CW complex with boundary operator and a discrete Morse function .

All manifolds and CW complexes are locally contractible, but in general not contractible.

These spaces are CW complexes.

Algebraic topologists work with compactly generated spaces, CW complexes, or spectra.

Auxiliary constructions that yield spaces that are not CW complexes must be used on occasion.

These three definitions are in fact equivalent for H-spaces that are CW complexes.

A CW complex X is coherent with its family of n-skeletons X.