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The Hahn-Mazurkiewicz theorem states that a space $X$ is a Peano Space if and only if $X$ is compact, connected and locally connected. If anybody knows a book with a proof, please let me know. Thanks.

P.S. (added by t.b.) A Peano space is a topological space which is the continuous image of the unit interval.

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2 Answers 2

up vote 7 down vote accepted

Hocking and Young, Topology also has a proof, theorem 3-30, page 129. Visible in Google Books.

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Thanks alot!!! :) –  Tau May 17 '11 at 12:23

Read the section on Peano spaces in General Topology by Stephen Willard.

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