Re: No homeomorphism (0,1) <--> [0,1]
- From: mstemper@xxxxxxxxxxxxxxxx (Michael Stemper)
- Date: Thu, 8 Sep 2005 12:56:57 -0500
In article <dfpqju$1c3a$1@xxxxxxxxxxxxxxxxxx>, Arturo Magidin writes:
>>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.
>Point the second: I thought about that (and, of course, compactness);
>but is it reasonable that someone who only knows the definitions of
>homeomorphism and continuity will be familiar with (i) the notion of
>connectedness; and (ii) that connectedness is a homeomorphic
>invariant?
Whether or not it's reasonable, I couldn't say. However, I can say that
I don't know them.
I this one of those exercises that Knuth would have marked with a 40 or so?
--
Michael F. Stemper
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