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Results tagged with gn.general-topology
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user 106622
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
4
votes
0
answers
70
views
"Robust" Noninjectivity of a Continuous Mapping of a Sphere into the Plane
Let $X=\mathbb{S}^2$ and $Y=\mathbb{R}^2$ and $f:X\to Y$ a continuous mapping. Is it true that there must exist a nonempty set $V\subset f(X)$, open in $f(X)$ (in the subspace topology), such that eac …
- 113
7
votes
1
answer
537
views
In a Polish space, is every analytic set the continuous image of a Borel set from the same P...
I'm confused by a subtle point in the definition of analytic sets. Suppose I have a Polish space $X$. Now I start with the collection of Borel sets in $X$ and take all their continuous images in $X$. …
- 113