Fibration

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.

Weaker properties

 * Weak fibration (also called Serre fibration)