Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Recall that we call a map $i: A \rightarrow X$ a cofibration if it has the homotopy extension property. We will say a pointed space $X$ is well-pointed, if the inclusion of the basepoint $\{ * \} \hookrightarrow X$ is a cofibration.

A pointed cofibration $i: A \rightarrow X$ is a based map of pointed spaces that has the homotopy extension property with respect to homotopies respecting the basepoint. Note that a cofibration is always a pointed cofibration, but the converse is not true.

It is stated in May's "Concise Course in Algebraic Topology", although not proved, that if a map of well-pointed spaces is a pointed cofibartion, then it is already a cofibration. I've been trying to do it on my own using "the box method", but it didn't lead me anywhere.

How does one go to prove such statements? Is there any general method, any useful tricks?

I assume that all spaces are compactly generated weakly Hausdorff.

share|improve this question

1 Answer 1

up vote 0 down vote accepted
+100

This is lemma 1.3.4 in May's "More concise algebraic topology", it looks very technical.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.