Weak fibration

This article defines a property of continuous maps between topological spaces

Definition

A continuous map $p:E\to B$ is termed a weak fibration or a Serre fibration if given any map $F:I^n\times I\to B$ and a map $\tilde{f}:I^n\to E$ such that $p(\tilde{f}(x))=f(x,0)$, there exists a map $\tilde{F}:I^n\times I\to E$ satisfying:

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