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

mstemper@xxxxxxxxxxxxxxxx (Michael Stemper) writes:

>>> 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.
[suggested answer]
>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.

Hmm. Are you *sure* you haven't learned anything about, say,
sequences in a metric space, their convergence and their non-
convergence? Because, if you have, I think I can give you a
suggestion.

Lee Rudolph (which might even be correct)
.

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