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Asking for reference:

X is a Hausdorff topological space and it is path-connected, then it is arcwise-connected.

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path-connected and arc-connected are not synonyms, as the latter requires the path to be a homeomorphism to its image, see eg en.wikipedia.org/wiki/… – David Roberts Jul 20 2011 at 8:00
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 This is more appropriate for math.stackexchange since it is actually an exercise in general topology. – Gjergji Zaimi Jul 20 2011 at 8:00
Also, this is question might be better off at math.stackexchange.com. – David Roberts Jul 20 2011 at 8:01
Snap! . – David Roberts Jul 20 2011 at 8:01
It might be some help to see the Hahn-Mazurkiewicz theorem first... – Gjergji Zaimi Jul 20 2011 at 8:08

closed as too localized by Gjergji Zaimi, David Roberts, S. Carnahan♦ Jul 20 2011 at 8:13

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