Higher-dimensional Bruckner-Garg type theorem |
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Authors: | Hisao Kato |
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Institution: | Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan |
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Abstract: | In this paper, we investigate several properties of maps from a compactum X to an n-dimensional (combinatorial) manifold Mn. We introduce the notions of stable point and locally extreme point of map, and we prove a higher-dimensional Bruckner-Garg type theorem for the fiber structure of a generic map in the space C(X,Mn) of maps from a compactum X with dimX?n to an n-dimensional manifold Mn (n?1). As applications, we also study the spaces of Bing maps, Lelek maps, k-dimensional maps and Krasinkiewicz maps in C(X,Mn). |
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Keywords: | primary 54C35 54F45 secondary 54F15 57Q65 |
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