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

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

I think this should be:

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

Agree. The two ${\displaystyle f}$'s need to be distinguished. To keep consistency with the diagram in the visualization section, I am changing the maps ${\displaystyle X\rightarrow Y}$ to ${\displaystyle {\tilde {f}}}$ (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)