# Ehresmann's fibration theorem for CW or simplicial complexes

Is there an analogue of Ehresmann fibration theorem for (finite) CW complexes ?

Note is not true that an open surjective (necessary proper) cellular map of finite CW or simplicial complexes is necessarily a Serre fibration: ramified coverings of surfaces are counterexamples, as pointed out in comments.

• A ramified cover between surfaces is open, and it is not a Serre fibration right? Dec 19, 2021 at 20:04
• I'm probably missing something but why say $z^2:\mathbb{C}\to\mathbb{C}$ is not a Serre fibration ? It does have the path lifting property, right, though ? By the way, I forgot to say "surjective" and now I added it. Dec 20, 2021 at 11:52
• Its fibres do not have constant (weak) homotopy type. Dec 20, 2021 at 12:12
• sorry, of course... i'll edit the question accordingly. Dec 20, 2021 at 19:22