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 &#124; 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)