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1d
accepted Is the intersection of two locally compact locally compact?
1d
asked Is the intersection of two locally compact 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
Apr
9
revised Is the cartesian product of homeomorphisms again a homeomorphism?
added 2 characters in body
Apr
9
answered Is the cartesian product of homeomorphisms again a homeomorphism?
Apr
8
comment Is the cartesian product of homeomorphisms again a homeomorphism?
What about a categorical argument? It's very simple.
Mar
30
awarded  Commentator
Mar
30
comment why natural transformatoins are also called “morphisms” of functors?
Maybe what you're looking for is in Exercise I.4.5 of Categories for the working mathematician.
Mar
14
awarded  Teacher
Mar
13
accepted “for almost all” symbol
Mar
13
asked “for almost all” symbol
Mar
7
awarded  Critic
Mar
7
comment Examples of colimits in a category of categories
Your question reminds me this paper. They give some examples of coequalizers in $\mathbf{Cat}$.
Mar
7
answered Problem book on general topology
Mar
6
comment Question of regular open
$U(A)=\cup\{U \text{ open}\mid A\subseteq U\}$?
Mar
6
comment Properties of Closure
This is not true. Consider $\mathbf{R}$ with the usual topology. Let $A:=[0,1)$. Then $(\bar{A})^c=(-\infty,0)\cup(1,\infty)$, but $\bar{A^c}=(-\infty,0]\cup[1,\infty)$.
Feb
4
comment How to show the standard $n$-simplex is homeomorphic to the $n$-ball
There is a generalization of this in Bredon's Topoloy and geometry, Proposition 16.4, page 56. The proposition says: ''A compact convex body $C$ in $\mathbf{R}^n$ with nonempty interior is homeomorphic to the closed $n$-ball''.