Fibration

This article defines a property of continuous maps between topological spaces

Definition

A continuous map $p:E\to B$ of topological spaces is termed a fibration or is said to have the homotopy lifting property if it is surjective and, given any map $F:X\times I\to B$ and a map $\tilde{f}:X\to E$ such that $p(\tilde{f}(x))=f(x,0)$, there exists a map $\tilde{F}:X\times I\to E$ satisfying:

• $p\circ \tilde{F}=F$
• $F(x,0)=\tilde{f}(x)$

This is dual to the notion of a cofibration.

Relation with other properties

Weaker properties

• Weak fibration (also called Serre fibration)