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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 29th 2019
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   Author: David_Corfield
   Format: MarkdownItexA stub here. Is there a ready example? <a href="https://ncatlab.org/nlab/revision/codense+subspace/1">v1</a>, <a href="https://ncatlab.org/nlab/show/codense+subspace">current</a>

   A stub here. Is there a ready example?

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorRichard Williamson
   • CommentTimeJan 29th 2019
   • (edited Jan 29th 2019)
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   Author: Richard Williamson
   Format: MarkdownItexIt will have to be non-$T_1$. The [[Sierpinski space]] with the closed point as $Y$ would be the minimal example I think, if not very interesting.

   It will have to be non-$T_1$. The Sierpinski space with the closed point as $Y$ would be the minimal example I think, if not very interesting.

3. • CommentRowNumber3.
   • CommentAuthorAli Caglayan
   • CommentTimeJan 29th 2019
   • (edited Jan 29th 2019)
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   Author: Ali Caglayan
   Format: MarkdownItexThere are probably a lot of examples with finite topological spaces, I don't know if they are interesting though. Oh and every space should be codense in itself?

   There are probably a lot of examples with finite topological spaces, I don’t know if they are interesting though. Oh and every space should be codense in itself?

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 29th 2019
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   Author: David_Corfield
   Format: MarkdownItexSo no intuitive story such as in the dense case of how behaviour on $\mathbb{Q}$ determines behaviour on $\mathbb{R}$?

   So no intuitive story such as in the dense case of how behaviour on $\mathbb{Q}$ determines behaviour on $\mathbb{R}$?

5. • CommentRowNumber5.
   • CommentAuthorTim_Porter
   • CommentTimeJan 29th 2019
   • (edited Jan 29th 2019)
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   Author: Tim_Porter
   Format: MarkdownItexA quick search came up with that the axiom of choice is equivalent to every non-empty space having a codense T_0 subspace. The name of McCarten was mentioned. There is a related notion in locale theory see http://www.mat.uc.pt/preprints/ps/p1445.pdf

   A quick search came up with that the axiom of choice is equivalent to every non-empty space having a codense T_0 subspace. The name of McCarten was mentioned.

   There is a related notion in locale theory see http://www.mat.uc.pt/preprints/ps/p1445.pdf