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Separation of homogeneous connected locally compact spaces.
- Source :
-
Proceedings of the American Mathematical Society, Series B . 3/5/2024, Vol. 11, p36-46. 11p. - Publication Year :
- 2024
-
Abstract
- We prove that any region \Gamma in a homogeneous n-dimensional and locally compact separable metric space X, where n\geq 2, cannot be irreducibly separated by a closed (n-1)-dimensional subset C with the following property: C is acyclic in dimension n-1 and there is a point b\in C\cap \Gamma having a special local base \mathcal B_C^b in C such that the boundary of each U\in \mathcal B_C^b is acyclic in dimension n-2. In case X is strongly locally homogeneous, it suffices to have a point b\in C\cap \Gamma with an ordinary base \mathcal B_C^b satisfying the above condition. The acyclicity means triviality of the corresponding Čech cohomology groups. This implies all known results concerning the separation of regions in homogeneous connected locally compact spaces. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 23301511
- Volume :
- 11
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society, Series B
- Publication Type :
- Academic Journal
- Accession number :
- 175851233
- Full Text :
- https://doi.org/10.1090/bproc/207