Difference between revisions of "Talk:Nowhere-dense set"
From Encyclopedia of Mathematics
(Or only if Hausdorff?) |
(Yes, only if Hausdorff) |
||
| Line 3: | Line 3: | ||
"if infinitely many factors are non compact, then any compact subset of X is nowhere dense" — really so? Or only if Hausdorff? --[[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 20:13, 22 September 2012 (CEST) | "if infinitely many factors are non compact, then any compact subset of X is nowhere dense" — really so? Or only if Hausdorff? --[[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 20:13, 22 September 2012 (CEST) | ||
| + | Yes, only if Hausdorff; otherwise a compact set can be dense! I have a counterexample. --[[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 08:45, 23 September 2012 (CEST) | ||
Latest revision as of 06:45, 23 September 2012
The original article uses the terminology boundary set for sets which are complements of dense sets. Since I never heard it before and I could not find it in a textbook, I have omitted it. Camillo (talk) 19:15, 22 September 2012 (CEST)
"if infinitely many factors are non compact, then any compact subset of X is nowhere dense" — really so? Or only if Hausdorff? --Boris Tsirelson (talk) 20:13, 22 September 2012 (CEST) Yes, only if Hausdorff; otherwise a compact set can be dense! I have a counterexample. --Boris Tsirelson (talk) 08:45, 23 September 2012 (CEST)
How to Cite This Entry:
Nowhere-dense set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Nowhere-dense_set&oldid=28114
Nowhere-dense set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Nowhere-dense_set&oldid=28114