A doubt in Munkres' Topology.

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On pg. 343 of Munkres' Topology (Second Edition), there is a diagram given that I am having problems understanding. This diagram is Figure 51.7.

Why are the paths $i$ and $e_0$ defined from $I$ to $I$? Shouldn't they mappings from $I$ to $X$?

Sorry I don't have a smartphone right now; I would have attached a photo of the diagram if I did.

Thank you.