Weak fibration

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:


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