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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 17th 2017
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   Author: Urs
   Format: MarkdownItexwrote out statement and proof that _[[locally compact and sigma-compact spaces are paracompact]]_

   wrote out statement and proof that locally compact and sigma-compact spaces are paracompact

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeMay 17th 2017
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   Author: Todd_Trimble
   Format: MarkdownItexI replaced the \backslash's by \setminus's, but feel free to revert if you don't like that.

   I replaced the \backslash’s by \setminus’s, but feel free to revert if you don’t like that.

3. • CommentRowNumber3.
   • CommentAuthorChickenNinja123
   • CommentTimeOct 27th 2018
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   Author: ChickenNinja123
   Format: MarkdownItexChanged the wording of the definition for locally compact; it looked like the definition of a regular space. <a href="https://ncatlab.org/nlab/revision/diff/locally+compact+and+sigma-compact+spaces+are+paracompact/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/locally+compact+and+sigma-compact+spaces+are+paracompact/8">v8</a>, <a href="https://ncatlab.org/nlab/show/locally+compact+and+sigma-compact+spaces+are+paracompact">current</a>

   Changed the wording of the definition for locally compact; it looked like the definition of a regular space.

   diff, v8, current

4. • CommentRowNumber4.
   • CommentAuthorGuest
   • CommentTimeJul 2nd 2019
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   Author: Guest
   Format: TextConcerning Lemma 1.1: In a puristic sense I would prefer to keep to the definition of `locally compact' that requires only that each point possesses a neighbourhood base consisting of compact sets. Supposing this, the assertion of the lemma will have to be modified as follows. There exist an open covering {U_n; n \in \N} of X and a sequence (V_n)_{n\in\N} of compact sets such that U_n \subseteq V_n \subseteq U_{n+1} for all n \in \N. The proof is essentially the same as given on the page. Jürgen Voigt, Dresden

   Concerning Lemma 1.1: In a puristic sense I would prefer to keep to the definition of `locally compact' that requires only that each point possesses a neighbourhood base consisting of compact sets. Supposing this, the assertion of the lemma will have to be modified as follows.
   
   There exist an open covering {U_n; n \in \N} of X and a sequence (V_n)_{n\in\N} of compact sets such that U_n \subseteq V_n \subseteq U_{n+1} for all n \in \N.
   
   The proof is essentially the same as given on the page.
   
   Jürgen Voigt, Dresden
5. • CommentRowNumber5.
   • CommentAuthorGuest
   • CommentTimeJul 3rd 2019
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   Author: Guest
   Format: TextHere is a supplement to my previous comment. From the property I indicated as the assertion I cannot deduce that the space is paracompact (which is the main issue of the page). Nevertheless I think that my contribution is of some value. On the page "locally compact topological space" I have the information that `Def. 2.2 = Def. 2.1 + regular'. Jürgen Voigt, Dresden

   Here is a supplement to my previous comment. From the property I indicated as the assertion I cannot deduce that the space is paracompact (which is the main issue of the page). Nevertheless I think that my contribution is of some value. On the page "locally compact topological space" I have the information that `Def. 2.2 = Def. 2.1 + regular'.
   
   Jürgen Voigt, Dresden
6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJul 4th 2019
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   Author: Urs
   Format: MarkdownItexJust to say that you may feel free to edit the entry. It's one of those fine-tuning issues in the definitions of basic topology and somebody made a choice at some point, probably it was me here. But that doesn't preclude further discussion of alternative approaches to be included, on this page and possibly on other related pages, and to highlight their advantages, if that's what you feel one should do. Myself, I have no spare time for this at the moment, so you shouldn't wait for any comments from me, let alone my approval. But since this is about basic textbook toplogy, nothing here should be controversial and I trust that you and other people who care can make a nice edit to whatever page is in need of such.

   Just to say that you may feel free to edit the entry.

   It’s one of those fine-tuning issues in the definitions of basic topology and somebody made a choice at some point, probably it was me here. But that doesn’t preclude further discussion of alternative approaches to be included, on this page and possibly on other related pages, and to highlight their advantages, if that’s what you feel one should do.

   Myself, I have no spare time for this at the moment, so you shouldn’t wait for any comments from me, let alone my approval. But since this is about basic textbook toplogy, nothing here should be controversial and I trust that you and other people who care can make a nice edit to whatever page is in need of such.