Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
  
  
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 29th 2019
   • PermaLink
   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)
   • PermaLink
   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-. The Sierpinski space with the closed point as would be the minimal example I think, if not very interesting.

3. • CommentRowNumber3.
   • CommentAuthorAli Caglayan
   • CommentTimeJan 29th 2019
   • (edited Jan 29th 2019)
   • PermaLink
   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
   • PermaLink
   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 determines behaviour on ?

5. • CommentRowNumber5.
   • CommentAuthorTim_Porter
   • CommentTimeJan 29th 2019
   • (edited Jan 29th 2019)
   • PermaLink
   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