Re: No homeomorphism (0,1) <--> [0,1]

In article <3ob7q4F54kquU1@xxxxxxxxxxxxxx>, Jose Carlos Santos writes:
>On 08-09-2005 17:34, Michael Stemper wrote:
>
>> I'm trying to prove that there isn't a homeomorphism between [0,1]
>> and (0,1), and I'm stuck. What I know so far is the definitions of
>> homeomorphism and continuity.
>
>Suppose that there was a homeomorphism f:[0,1] --> ]0,1[. It's
>continuous, and so, by Weierstrass' theorem,

Thanks for the reply. However, all that I've learned so far is the
definitions of metric space, continuity, and homeomorphism. I certainly
haven't encountered this theorem yet.

For anybody playing along at home, this exercise is a post script
to Exercise C, Chapter III, in _Topology_, by George McCarty.


--
Michael F. Stemper
#include <Standard_Disclaimer>
This sentence no verb.

.

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