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Apr 24, 2010 at 0:04 vote accept zeb
Apr 23, 2010 at 22:29 comment added Ady @Petya In fact, a (planar) Cook continuum without a point would be such a counterexample.
Apr 23, 2010 at 19:43 comment added Sergei Ivanov No, fold it twice and contract the half-circle.
Apr 23, 2010 at 19:38 comment added Petya It seems that a circle without a point is also a counter-example to the first question.
Apr 23, 2010 at 19:13 history edited Sergei Ivanov CC BY-SA 2.5
added counter-example to the second question
Apr 23, 2010 at 8:02 history answered Sergei Ivanov CC BY-SA 2.5