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Results tagged with gn.general-topology
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user 3948
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
6
votes
0
answers
366
views
Whitney approximation without second countable
One version of Whitney's approximation theorem states the following:
Let $N$ be a smooth, Hausdorff, second-countable (or paracompact) manifold, then given any continuous function $F:N\to \mathbb{ …
- 39.1k
3
votes
0
answers
73
views
Equivalence relation induced by Kolmogorov quotients
Recall: given a (possibly non-$T_0$) topological space $X$, its Kolmogorov quotient $KX$ is the $T_0$ topological space formed by $X/\sim$ where $x\sim y$ if they are topologically indistinguishable. …
- 39.1k
156
votes
4
answers
18k
views
Does there exist a bijection of $\mathbb{R}^n$ to itself such that the forward map is connec...
Let $(X,\tau), (Y,\sigma)$ be two topological spaces. We say that a map $f: \mathcal{P}(X)\to \mathcal{P}(Y)$ between their power sets is connected if for every $S\subset X$ connected, $f(S)\subset Y$ …
- 39.1k