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RESEARCH PRODUCT
Isometrically Homogeneous and Topologically Homogeneous Continua
Janusz R. Prajssubject
Pure mathematicstopological groupsemi-indecomposableGeneral Mathematics010102 general mathematicsisometrically homogeneouscontinuumample01 natural sciences010101 applied mathematicsindecomposablehomogeneousHomogeneousaposyndetic0101 mathematicsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 | Indiana University Mathematics Journal |