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What about 2S where S is uncountable? Should that be included among what are called Cantor spaces? (It can be shown that every Boolean space, i.e., every totally disconnected compact Hausdorff space, is a compact subspace of one of these.) Michael Hardy 03:29, 1 Nov 2003 (UTC)
I was wondering the same thing. And this may seem unnecessarily fussy to remark, but if Cantor space is unique up to homeomorphism, why does this article keep referring to it with the indefinite article? I understand that there are many distinct, homeomorphic realisations of the Cantor set (space), but when talking about it where it doesn't matter what the concrete representation of it is, can't it just be called "the Cantor space"? We talk about "the long line", or "the Sierpinski space", not "a long line" or "a Sierpinski space". Revolver
I hadn't even seen this talk page when I created the article Cantor cube! Well, see it for arbitrary products of 2. Melchoir 21:14, 6 July 2006 (UTC)
I seriously question the term "Cantor space" being used to mean -- as it is defined here -- a topological space homeomorphic to the Cantor set.
In my 40 years of being a topologist, I have never encountered a space homeomorphic to the Cantor set being called anything but a "Cantor set". (The original, traditional Cantor set is called the "middle-thirds Cantor set".)
I strongly urge this article to bring itself in line with prevailing terminology. Daqu ( talk) 07:18, 26 May 2008 (UTC)
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What about 2S where S is uncountable? Should that be included among what are called Cantor spaces? (It can be shown that every Boolean space, i.e., every totally disconnected compact Hausdorff space, is a compact subspace of one of these.) Michael Hardy 03:29, 1 Nov 2003 (UTC)
I was wondering the same thing. And this may seem unnecessarily fussy to remark, but if Cantor space is unique up to homeomorphism, why does this article keep referring to it with the indefinite article? I understand that there are many distinct, homeomorphic realisations of the Cantor set (space), but when talking about it where it doesn't matter what the concrete representation of it is, can't it just be called "the Cantor space"? We talk about "the long line", or "the Sierpinski space", not "a long line" or "a Sierpinski space". Revolver
I hadn't even seen this talk page when I created the article Cantor cube! Well, see it for arbitrary products of 2. Melchoir 21:14, 6 July 2006 (UTC)
I seriously question the term "Cantor space" being used to mean -- as it is defined here -- a topological space homeomorphic to the Cantor set.
In my 40 years of being a topologist, I have never encountered a space homeomorphic to the Cantor set being called anything but a "Cantor set". (The original, traditional Cantor set is called the "middle-thirds Cantor set".)
I strongly urge this article to bring itself in line with prevailing terminology. Daqu ( talk) 07:18, 26 May 2008 (UTC)