Talk:Homotopy extension property

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Definition is somewhat awkward, but this is the best way to phrase it. Also someone should make algebraic-topology stub type. 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 (talkcontribs) 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?[edit]

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)