Re: Compact subsets of {0,1}^N

From: David Bernier <david250@xxxxxxxxxxxx>
Newsgroups: sci.math
Subject: Re: Compact subsets of {0,1}^N

William Elliot wrote:

>>A closed nonnul subset K without isolated points of S = {0,1}^N
>>is homeomorphic to S.

> There was a thread in sci.math.research in Dec. 2004:
> ``Brouwer's characterization of Cantor set" started
> by Jorge Buescu.

> Lee Rudolph wrote there in part:

> ``Ah, but Zentralblatt does (at least, now that it incorporates
> JFM). My German is not up to the task of deciding, for certain,
> whether the following reference is what you need, but (a) it seems
> likely, and (b) if not, and if you can find the reference itself,
> then there might be something in its bibliography that *is* what
> you need.

Impossible to tell. Proofs of the Cantor set theorems abound.
The thread is attempt to proof equivalent theorems, not about
the Cantor set but about the homeomorphic space {0,1}^N, from
within the space as a topological space.

I pulled down the thread from Google, but ever since they went to
corporate stock company, they revised their software according to
requirements of the mega-money makers, which alas means that what work
well, now works lousy and while they were "improving" they broke stuff.
For example, the tree listing of posts is now defunct and this particular
thread was garbled with other stuff from totally unrelated source.

Anyway, thanks for your concern.

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