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 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 sheaves 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.
   • CommentAuthorAndrew Stacey
   • CommentTimeSep 19th 2011
   • PermaLink
   Author: Andrew Stacey
   Format: MarkdownItexI want to refer to that classic result about continuous bijections from compact spaces to Hausdorff spaces, but I can't find it at [[Hausdorff space]], [[compact space]], or [[compact Hausdorff space]]. Do we have it somewhere else? (If so, I'll add the links to those pages as it ought to be findable from them) If not, where should it go? As it's a simple proof, if we need to put the statement in then I may as well include the proof, and then it feels as though it would be better on its own page - most people would find the proof a distraction so it should be hidden away. In that case, what's a good name for the page? Is this result attributed to anyone in particular?

   I want to refer to that classic result about continuous bijections from compact spaces to Hausdorff spaces, but I can’t find it at Hausdorff space, compact space, or compact Hausdorff space.

   Do we have it somewhere else? (If so, I’ll add the links to those pages as it ought to be findable from them)

   If not, where should it go? As it’s a simple proof, if we need to put the statement in then I may as well include the proof, and then it feels as though it would be better on its own page - most people would find the proof a distraction so it should be hidden away. In that case, what’s a good name for the page? Is this result attributed to anyone in particular?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 19th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItex> Do we have it somewhere else? I don't think we do. > it would be better on its own page sounds good > Is this result attributed to anyone in particular? Even if it is, may I suggest that we give the page with the proof a descriptive title rather than name it after some person? I think that is more useful in the long run. We can still honor whoever deserves honorship in the entry content.

   Do we have it somewhere else?

   I don’t think we do.

   it would be better on its own page

   sounds good

   Is this result attributed to anyone in particular?

   Even if it is, may I suggest that we give the page with the proof a descriptive title rather than name it after some person? I think that is more useful in the long run. We can still honor whoever deserves honorship in the entry content.

3. • CommentRowNumber3.
   • CommentAuthorAndrew Stacey
   • CommentTimeSep 19th 2011
   • PermaLink
   Author: Andrew Stacey
   Format: MarkdownItexTurns out we *did* have it! I was cleaning up some references and found the following at [[continuous map]]: > Every continuous map from a compact space to a [[Hausdorff space]] is both closed and proper. However, that page was a bit messy and by then I'd written [[map+from+compact+space+to+Hausdorff+space]]. I cleaned up [[continuous map]] a bit as well.

   Turns out we did have it! I was cleaning up some references and found the following at continuous map:

   Every continuous map from a compact space to a Hausdorff space is both closed and proper.

   However, that page was a bit messy and by then I’d written map+from+compact+space+to+Hausdorff+space. I cleaned up continuous map a bit as well.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeApr 13th 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItex[beware that this is a reply to a 6 year old message in #3 from somebody who is no longer active here] I have * renamed the entry "map from compact space to Hausdorff space" into _[[maps from compact spaces to Hausdorff spaces are closed and proper]]_ * expanded the proof, by including pointers to the lemmas that it uses, namely * [[closed subsets of compact spaces are compact]] * [[continuous images of compact spaces are compact]] * [[compact subspaces of Hausdorff spaces are closed]] * re-arranged a little

   [beware that this is a reply to a 6 year old message in #3 from somebody who is no longer active here]

   I have

   • renamed the entry “map from compact space to Hausdorff space” into maps from compact spaces to Hausdorff spaces are closed and proper

   • expanded the proof, by including pointers to the lemmas that it uses, namely

     • closed subsets of compact spaces are compact

     • continuous images of compact spaces are compact

     • compact subspaces of Hausdorff spaces are closed

   • re-arranged a little