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Difference between revisions of "Talk:Compact-open topology"

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(That is what is in the original English text)
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"where $X_i$ is a compact Hausdorff subset of $X$" — really? I never saw "Hausdorff set", only space... [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 18:33, 28 December 2016 (CET)
 
"where $X_i$ is a compact Hausdorff subset of $X$" — really? I never saw "Hausdorff set", only space... [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 18:33, 28 December 2016 (CET)
 
:That is what is in the original English text.  I presume that the intended meaning is that $X_i$ is a subset of $X$ which is compact and Hausdorff with respect to the inherited topology.  The wording "subspace" rather than "subset" might be clearer.  The question of whether Hausdorff is a usual requirement in this situation is doubtful: Kelley for example does not include this.  [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 18:52, 28 December 2016 (CET)
 
:That is what is in the original English text.  I presume that the intended meaning is that $X_i$ is a subset of $X$ which is compact and Hausdorff with respect to the inherited topology.  The wording "subspace" rather than "subset" might be clearer.  The question of whether Hausdorff is a usual requirement in this situation is doubtful: Kelley for example does not include this.  [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 18:52, 28 December 2016 (CET)
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::Yes, I also feel the doubt: what for to require it? [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 07:01, 29 December 2016 (CET)
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:::It is also not mentioned in the article on [[Space of mappings, topological]], so I propose to remove the word "Hausdorff".  [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 08:30, 29 December 2016 (CET).
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::::Yes I did. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 08:44, 29 December 2016 (CET)

Latest revision as of 07:44, 29 December 2016

"where $X_i$ is a compact Hausdorff subset of $X$" — really? I never saw "Hausdorff set", only space... Boris Tsirelson (talk) 18:33, 28 December 2016 (CET)

That is what is in the original English text. I presume that the intended meaning is that $X_i$ is a subset of $X$ which is compact and Hausdorff with respect to the inherited topology. The wording "subspace" rather than "subset" might be clearer. The question of whether Hausdorff is a usual requirement in this situation is doubtful: Kelley for example does not include this. Richard Pinch (talk) 18:52, 28 December 2016 (CET)
Yes, I also feel the doubt: what for to require it? Boris Tsirelson (talk) 07:01, 29 December 2016 (CET)
It is also not mentioned in the article on Space of mappings, topological, so I propose to remove the word "Hausdorff". Richard Pinch (talk) 08:30, 29 December 2016 (CET).
Yes I did. Boris Tsirelson (talk) 08:44, 29 December 2016 (CET)
How to Cite This Entry:
Compact-open topology. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compact-open_topology&oldid=40081