0000000000344166

AUTHOR

Keith Whittington

showing 2 related works from this author

Filament sets and homogeneous continua

2007

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.

SubcategoryAmpleContinuum (topology)010102 general mathematicsMathematical analysisMathematics::General TopologySpace (mathematics)01 natural sciences010101 applied mathematicsProtein filamentQuantitative Biology::Subcellular ProcessesMathematics::Algebraic GeometryGeneral theoryHomogeneousContinuumFilamentHomogeneousGeometry and Topology0101 mathematicsIndecomposable moduleMathematicsTopology and its Applications
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Filament sets and decompositions of homogeneous continua

2007

Abstract This paper applies the concepts introduced in the article: Filament sets and homogeneous continua [J.R. Prajs, K. Whittington, Filament sets and homogeneous continua, Topology Appl. 154 (8) (2007) 1581–1591, doi:10.1016/j.topol.2006.12.005 ] to decompositions of homogeneous continua. Several new or strengthened results on aposyndesis are given. Newly defined decompositions are discussed. A proposed classification scheme for homogeneous continua is shown to be mostly invariant under Jones' aposyndetic decomposition.

010102 general mathematicsMathematical analysisClassification scheme01 natural sciences010101 applied mathematicsProtein filamentHomogeneousContinuumFilamentHomogeneousGeometry and Topology0101 mathematicsInvariant (mathematics)MathematicsTopology and its Applications
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