List questions from homotopy-extension-property | MathQA

Properties of covering spaces replacing base points by contractible subspaces

Published on 23 Feb 2026 - 4:48

Homotopy Extension and Deformation Retracts

Published on 23 Feb 2026 - 4:45

Question in Hatcher's Algebraic Topology Exercise 0.27

Published on 23 Feb 2026 - 4:45

Proof that higher homotopy groups of kan complexes are abelian using Eckmann-Hilton

Published on 23 Feb 2026 - 4:48

All finite path connected CW complexes are homotopy equivalent to a CW complex with only one 0-cell.

Published on 23 Feb 2026 - 4:49

$(M_f, X \cup Y)$ has the homotopy extension property

Published on 23 Feb 2026 - 4:46

Proving that two formulations of the Homotopy Extension Property via diagrams, are equivalent.

Published on 23 Feb 2026 - 3:00

Show that either $X$ or $Z$ is homotopy equivalent to a point.

Published on 23 Feb 2026 - 2:58

Hatcher Algebraic Topology 0.28

Published on 23 Feb 2026 - 4:45

Prove that it is NOT $F_{0} \simeq_{S_{1} \cup 2 S_{1}} F_{1}$ for $F(x, t)= e^{2\pi t i (|x|-1)} x$

Published on 23 Feb 2026 - 4:47

any cofibration $i:A \to B$ is a homeomorphism onto its image (question regarding the inverse map)

Published on 23 Feb 2026 - 4:47

If a homotopy can be extended to a neighborhood of a closed subspace of a normal space $X$, then it can be extended to all of $X$.

Published on 23 Feb 2026 - 4:47

Example where $(X,Y)$ and $(X,Z)$ have the homotopy extension property, but $(Y,Z)$ doesn't

Published on 23 Feb 2026 - 4:47

Where can I get an alternative proof of this characterisation of weak equivalences?

Published on 23 Feb 2026 - 4:47

When is a freely contractible space also based contractible?

Published on 23 Feb 2026 - 4:45