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 Yearling
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  • 40 votes cast
Jul
7
comment Closed Compact Subset of Product Space Must Have Empty Interior
This implies that the assumption that $K$ is closed is not necessary.
Jun
28
accepted Subadditivity inequality and power functions
Jun
28
comment The boundary of a closed subset $A$ of a compact connected hausdorff space
Duh for me. I missed that. Thanks.
Jun
28
accepted The boundary of a closed subset $A$ of a compact connected hausdorff space
Jun
27
comment The boundary of a closed subset $A$ of a compact connected hausdorff space
To prove that second lemma, he uses the first lemma, but I'm having trouble seeing why $C\cap B=\emptyset$ in the if part of that first lemma. In that lemma, the first one, $K$ is a compact subset of $X$, which is Hausdorff, and $B$ is $\partial K$ in $X$. In my question $X$ is Hausdorff, and compact and connected. If my $X$ is Hausdorff too, $A$ is compact too (because $A$ is closed in a compact) and my $C$ is a component of $A$, why there, in the if part of the first lemma, $C\cap\partial A=\emptyset$, but you prove that $C\cap\partial A\neq\emptyset$. What is going on?!
Jun
26
revised The boundary of a closed subset $A$ of a compact connected hausdorff space
deleted 2 characters in body
Jun
25
revised The boundary of a closed subset $A$ of a compact connected hausdorff space
added 3 characters in body
Jun
25
asked The boundary of a closed subset $A$ of a compact connected hausdorff space
Jun
12
accepted $\mathbb{I}\times\mathbb{Q}\cup\mathbb{Q}\times\mathbb{I}$ and connectedness
Jun
12
comment $\mathbb{I}\times\mathbb{Q}\cup\mathbb{Q}\times\mathbb{I}$ and connectedness
Sorry for not being clear. I've just edited my question in order to be clear.
Jun
12
revised $\mathbb{I}\times\mathbb{Q}\cup\mathbb{Q}\times\mathbb{I}$ and connectedness
added 175 characters in body
Jun
12
asked $\mathbb{I}\times\mathbb{Q}\cup\mathbb{Q}\times\mathbb{I}$ and connectedness
Jun
1
comment Showing one point compactification is unique up to homeomorphism
@BrianM.Scott, great! Very nice of you, by the way.
Jun
1
comment Showing one point compactification is unique up to homeomorphism
With respecto to the counterexample, a point is added to a space which is already compact. Should it have been non compact? Am I getting the question wrong?
May
28
accepted Is the intersection of two locally compact subspaces locally compact?
May
27
asked Is the intersection of two locally compact subspaces locally compact?
May
12
comment Complementary compactness
A space with the trivial topology is compact but not Hausdorff, not even $T_1$.
May
12
accepted Complementary compactness
May
12
awarded  Yearling
May
12
asked Complementary compactness