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Results tagged with gn.general-topology
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user 4281
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
5
votes
Accepted
Expressing any f(x,y) using only addition and unary functions?
This is "due in successively more exact forms to Kolmogorov, Arnol'd and a succession of mathematicians ending with Kahane", to quote T.W. Korner on the subject.
I am informed that the proof I met is …
- 1,771
4
votes
What should be taught in a 1st course on smooth manifolds?
This is in agreement with Igor's comment on Anton's answer, but became too long.
I'd say whatever approach you ultimately take, for a first-year grad course it surely has to be done 'properly', i.e. …
2
votes
2
answers
1k
views
When is the group of homeomorphisms of a compact space locally compact?
When is the group of homeomorphisms of
a compact space locally compact?
I am interested in finding out when the group of homeomorphisms of a compact topological space $X$ (with appropriate topo …
- 1,771
0
votes
Applications of connectedness
You can get the maximum principle for subharmonic functions: Write $F$ for the supremum of $f$ in $\Omega$, write $A$ for the set where $f = F$ and $B$ for the set where $f < F$. Then
$\Omega = A \cu …