Cofibration

In mathematics Kofaserungen are an important concept in algebraic topology.

Definition

A continuous map is a Kofaserung if it satisfies the Homotopieerweiterungseigenschaft, ie when it comes to continuous maps

With

( for by defined Inclusive ) will always be a continuous map

With

There.

If the inclusion of a sub-space, then this condition is equivalent to the fact that there is a retraction

There.

Examples

• The inclusion

• For every CW - complex and all is the inclusion

Kofaser

The homotopy Kofaser an ( arbitrary) continuous map is their Figure cone. For each ( generalized) homology theory one has a long exact sequence

If the picture is a Kofaserung, refers to the homotopy Kofaser as Kofaser.

If an inclusion is a Kofaserung, then the Kofaser is homotopy equivalent to the quotient space and it is