Filament local product structures in homogeneous continua
Volume 173 / 2023
Colloquium Mathematicum 173 (2023), 159-174
MSC: Primary 54F15; Secondary 54C65.
DOI: 10.4064/cm8629-3-2023
Published online: 8 May 2023
Abstract
This is a classifying study of homogeneous continua focused on decoding the structure of their neighborhoods. All non-locally-connected homogeneous continua have closed neighborhoods whose quotient space of components is homeomorphic to the Cantor set. Yet there are homogeneous non-locally-connected continua without neighborhoods homeomorphic to the product of a continuum and the Cantor set. The main result of this paper provides a useful criterion for identifying such neighborhoods. We show a number of applications of this result.
