Search results for "semi-indecomposable"
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Isometrically Homogeneous and Topologically Homogeneous Continua
2016
Based on the past study of homogeneous continua, this paper concludes that compact connected metric topological groups and isometrically homogeneous continua fall into the following three mutually disjoint classes: (1) indecomposable; (2) aposyndetic and semi-indecomposable; (3) mutually aposyndetic. Among all continua these are special classes with members having extremal properties. Indecomposable isometrically homogeneous continua are characterized as solenoids, and one-dimensional isometrically homogeneous continua are characterized as solenoids or circles. It is shown that path connected isometrically homogeneous continua are locally connected.
Semi-terminal continua in homogeneous spaces
2016
A semi-terminal continuum Y in a space X is defined by the condition that no two disjoint subcontinua of X intersect both Y and X-Y. Though numerous obvious examples of such continua can be found in arcs, trees and tree-like continua, these examples are related to the non-homogeneity of the space, and having semi-terminal continua in a homogeneous continuum is counter-intuitive. Recently, a large collection of homogeneous spaces with semi-terminal, non-terminal subcontinua has been found. This paper is devoted to studying these spaces and the general structure of homogeneous continua related to the presence of semi-terminal subcontinua.