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Nov 21, 2019 at 22:41 comment added H-H @Paul: Do you know any book that contains these theorems, thanks.
Sep 23, 2019 at 16:55 comment added Matthew Kvalheim For 1, why can you ensure that the preimage is connected? What about the map of the $3$ torus to the circle $S^1 \subset \Bbb C$ given by $(z_1, z_2, z_3)\mapsto z_1^2$, for which every level set has two connected components?
Feb 12, 2012 at 0:52 history edited John Pardon CC BY-SA 3.0
fixed spelling of Hurewicz
Apr 13, 2010 at 17:55 vote accept Steve
Apr 13, 2010 at 13:34 history edited Paul CC BY-SA 2.5
fixed typos
Apr 13, 2010 at 13:26 history edited Paul CC BY-SA 2.5
added 191 characters in body
Apr 13, 2010 at 13:01 history answered Paul CC BY-SA 2.5