2008/07/23 by Alexandre Karassev, Paweł Krupski, Karassev, A. +5
Mathematics · Medicine · #54F45 #55M10 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications
paper · pdf · doi:10.48550/arxiv.0807.3756
openalex publication_date 2008/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Vn-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.