The hyperspace of hereditarily decomposable subcontinua of a cube is the Hurewicz set |
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Authors: | Alicja Samulewicz |
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Institution: | Institute of Mathematics, Faculty of Mathematics and Physics, The Silesian University of Technology, ul. Kaszubska 23, 44-101 Gliwice, Poland |
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Abstract: | The hyperspaces of hereditarily decomposable continua and of decomposable subcontinua without pseudoarcs in the cube of dimension greater than 2 are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval 0,1]. Moreover, in such a cube, all indecomposable subcontinua form a homotopy dense subset of the hyperspace of (nonempty) subcontinua. |
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Keywords: | primary 54B20 57N20 secondary 54F45 54H05 |
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