CW-complex, Hausdorff space, second-countable space, sober space
connected space, locally connected space, contractible space, locally contractible space
Serre fibration $\Leftarrow$ Hurewicz fibration $\Rightarrow$ Dold fibration $\Leftarrow$ shrinkable map
A Serre fibration is a continuous map between topological spaces that has the right lifting property with respect to all inclusions of the form $i : \Delta^n \hookrightarrow \Delta^n \times I$ that include the standard topological $n$-simplex $\Delta^n \in$ Top as $\Delta^n \times \{0\}$.
This condition is a special case of that for a Hurewicz fibration.
The Serre fibrations serve as the abstract fibrations in the standard model structure on topological spaces.