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I'm interested in showing that $CX=\frac{I\times X}{\{1\}\times X}$ is contractible.

I defined the d.r $F(s,[t,x])=[(1-s)t+s,x]$ and the only missing part for me is to show that it is continuous. How do I do that?

I did see some related questions (example: J. J. Rotman's proof that the cone is contractible ), but couldn't understand completly why $F$ is continuous iff $F\circ(q×1)$ is continuous.

Also, is there a more traditional way to show the continuity?

Thanks

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TopologyGetsMeTired
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  • oh stop that, like I didn't see this question. I asked because I didn't understand it there, as i did mention in this thread. I'm allowed to ask for clarifications. plus i asked for a traditional way as well. – TopologyGetsMeTired May 08 '15 at 20:52
  • You need the result that a.r. cites at the end. It's not that easy, but, as a.r. writes in the beginning, that's just how it is. – Carsten S May 08 '15 at 21:01

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