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Tom Goodwillie
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The short down-to-earth answer is that if the inclusion $A\to X$ has the homotopy extension property then the answer is yes. This is covered in, for example, Chapter $0$ of Hatcher's book Algebraic Topology (available for free at his web site).

EDIT: My memory was inaccurate. As Ronnie Brown points out, this result is not there. It should be there, perhaps as an exercise: derive it from Corollary 0.21.

The short down-to-earth answer is that if the inclusion $A\to X$ has the homotopy extension property then the answer is yes. This is covered in, for example, Chapter $0$ of Hatcher's book Algebraic Topology (available for free at his web site).

The short down-to-earth answer is that if the inclusion $A\to X$ has the homotopy extension property then the answer is yes. This is covered in, for example, Chapter $0$ of Hatcher's book Algebraic Topology (available for free at his web site).

EDIT: My memory was inaccurate. As Ronnie Brown points out, this result is not there. It should be there, perhaps as an exercise: derive it from Corollary 0.21.

Source Link
Tom Goodwillie
  • 55.9k
  • 7
  • 151
  • 240

The short down-to-earth answer is that if the inclusion $A\to X$ has the homotopy extension property then the answer is yes. This is covered in, for example, Chapter $0$ of Hatcher's book Algebraic Topology (available for free at his web site).