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Results tagged with gn.general-topology
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user 50614
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
0
votes
0
answers
169
views
Problem of Thickening an Arc in a Topological $ 2 $-Manifold
Let $ M $ be a topological $ 2 $-manifold (possibly with boundary), $ C $ an arc in the interior of $ M $ (i.e., an injective continuous function from $ [- 1,1] $ into $ \operatorname{Int}(M) $), and …
- 1,396
3
votes
1
answer
144
views
Is $ {C_{c}}(G) $ a meager subset of $ {L^{2}}(G) $ for a second-countable locally compact H...
The following problem is a stumbling block in a research project that I am working on:
Problem. Let $ G $ be a second-countable locally compact Hausdorff group with a fixed Haar measure. Is it tru …
- 1,396
2
votes
2
answers
333
views
A Jordan Separation Theorem for Polyhedral Surfaces
Let me begin by defining what a polyhedral surface is.
A path-connected subset $ P $ of $ \mathbb{R}^{3} $ is called a polyhedral surface iff it is the union of a finite collection $ \mathcal{C} $ of …
- 1,396
13
votes
3
answers
816
views
Is there a Borel subset of $ \mathbb{R}^{2} $, with finite vertical cross-sections, whose pr...
This question is related to another one that I asked two days ago.
Question. Does there exist a Borel subset $ M $ of $ \mathbb{R}^{2} $ with
the following two properties?
The projecti …
- 1,396