Reference for a proof of the Hahn-Mazurkiewicz theorem

Question

The Hahn-Mazurkiewicz theorem states that a space $X$ is a Peano Space if and only if $X$ is compact, connected, locally connected, and metrizable. 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.

score 13 · Accepted Answer · answered May 17 '11 at 11:08

13

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

answered May 17 '11 at 11:08

Henno Brandsma

242,131

score 11 · Answer 2 · 2012-12-12T03:29:19.077

11

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

edited Dec 12 '12 at 03:29

answered May 17 '11 at 10:53

Reference for a proof of the Hahn-Mazurkiewicz theorem

2 Answers2

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