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Filament sets and homogeneous continua |
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| Authors: | Janusz R Prajs Keith Whittington |
| Institution: | a California State University Sacramento, Department of Mathematics and Statistics, 6000 J street, Sacramento, CA 95819, USA b University of Opole, Institute of Mathematics, ul. Oleska 48, 45-052 Opole, Poland c University of the Pacific, Stockton, CA 95211, USA |
| Abstract: | New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament, non-filament, and ample, with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces. |
| Keywords: | primary 54F15 secondary 54H15 |
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