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If two functions are homotopic must their mapping cylinders be also?

  1. Feb 9, 2013 #1
    Hey I feel like I understand the concept of two spaces being homotopic and I can "visualize" the concept because I think of one space kind of continuously morphing in to the other. But when it comes to thinking of homotopy between functions, I have a harder time. I was trying to think of a way to visualize things and the way I know to visualize a function is by looking at its mapping cylinder. So I was wondering, is it the case that if we can show the mapping cylinders of two functions are homotopic, that the functions themselves are homotopic?

    Does anyone have any good resources on things I can read that will help me understand homotopy between functions a little more intuitively? Or to understand the "link" between spaces being homotopic and functions being homotopic

    (I know the definitions, but I guess I just have a hard time visualizing functions being homotopic :( )
  2. jcsd
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