Algebraic Topology - 5.4 - Mapping Spaces and the Compact Open Topology

We prove the adjunction between Top(X,-) and X\times- at least on the level of sets.

[ДанилаШубин-ъъ]

Thank you very much! I really appreciate this work you've done!

Could you clarify, why do we care about evaluation map being continuous at all?

[thephysicistcuber]

3:32 I think we can just set K={x} and not need any assumptions on X.

EDIT: no you can't. You're gonna prove continuity in f and not joint continuity. Still local compactness of X and the assumption of T2 should be enough.