Generalized Cantor manifolds and homogeneity
| dc.creator | Karassev, A. | |
| dc.creator | Krupski, P. | |
| dc.creator | Todorov, V. | |
| dc.creator | Valov, V. | |
| dc.date | 2008-07-23 | |
| dc.date.accessioned | 2026-07-07T09:52:32Z | |
| dc.date.available | 2026-07-07T09:52:32Z | |
| dc.description | A classical theorem of Alexandroff states that every $n$-dimensional compactum $X$ contains an $n$-dimensional Cantor manifold. This theorem has a number of generalizations obtained by various authors. We consider extension-dimensional and infinite dimensional analogs of strong Cantor manifolds, Mazurkiewicz manifolds, and $V^n$-continua, and prove corresponding versions of the above theorem. We apply our results to show that each homogeneous metrizable continuum which is not in a given class $\mathcal C$ is a strong Cantor manifold (or at least a Cantor manifold) with respect to $\mathcal C$. Here, the class $\mathcal C$ is one of four classes that are defined in terms of dimension-like invariants. A class of spaces having bases of neighborhoods satisfying certain special conditions is also considered. | |
| dc.description | 26 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0807.3756 | |
| dc.identifier | http://arxiv.org/abs/0807.3756 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165628 | |
| dc.subject | General Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 54F45; 55M10 | |
| dc.title | Generalized Cantor manifolds and homogeneity | |
| dc.type | text |