Talk:Homotopy extension property

Definition

Definition is somewhat awkward, but this is the best way to phrase it. Also someone should make algebraic-topology stub type. 70.152.47.105 00:26, 13 February 2006 (UTC)

Given any continuous $f:X\to Y$, $g:A\to Y$ for which there is a homotopy $G:A\times I\to Y$ of $\mathbf {\mathit {f}}$ and $\mathbf {\mathit {g}}$...

Shouldn't this be $\mathbf {\mathit {f}} \mid A$ and $\mathbf {\mathit {g}}$ ? Metterklume 23:20, 16 July 2007 (UTC)

I think this should be:

Given any continuous $f:X\to Y$ and homotopy $G:A\times I\to Y$ with $G\mid A\times {0}=\mathbf {\mathit {f}} \mid A$, we can extend this to a homotopy $F:X\times I\to Y$ with $F\mid X\times {0}=\mathbf {\mathit {f}}$ and $F\mid A\times I=G$. —Preceding unsigned comment added by Thufir Hawat (talk • contribs) 21:31, 8 January 2008 (UTC)

Agree. The two $f$'s need to be distinguished. To keep consistency with the diagram in the visualization section, I am changing the maps $X\rightarrow Y$ to ${\tilde {f}}$ (i.e. adding the tilde). - Subh83 (talk | contribs) 22:38, 22 November 2011 (UTC)

Cofibrations are embeddings?

I don't think this is true for arbitrary spaces, does anyone have a reference? Money is tight (talk) 14:57, 26 January 2011 (UTC)