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I'm confused by Munkres' definition of the path product using the positive linear map. He defines the positive linear map $p: [a,b] \rightarrow [c,d]$ to be the unique map of the form $x \mapsto mx + k$ that carries $a$ to $c$ and $b$ to $d$. He says the following:

We can then describe the path product $f*g$ as follows: on $[0,\frac{1}{2}]$ it equals the positive linear map of $[0,\frac{1}{2}]$ to $[0,1]$ followed by $f$ and on $[\frac{1}{2},1]$ it equals the positive linear map of $[\frac{1}{2},1]$ to $[0,1]$ followed by $g$.

I feel the definition is unclear. What exactly does he mean "followed by $f$" and "followed by $g$"?

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    $\begingroup$ Okay I figured it out, by "followed by" he means function composition. I'll leave this question up in case anyone else ever gets confused by this ! $\endgroup$ – TuoTuo Jan 27 '16 at 0:09
  • $\begingroup$ But you should write an official answer and accept it to to clear the question from the unanswered queue. $\endgroup$ – Paul Frost Jan 13 at 10:12

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