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:

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