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Abstrakty
We prove that the set of all Krasinkiewicz maps from a compact metric space to a polyhedron (or a 1-dimensional locally connected continuum, or an n-dimensional Menger manifold, n ≥ 1) is a dense Gδ-subset of the space of all maps. We also investigate the existence of surjective Krasinkiewicz maps from continua to polyhedra.
Wydawca
Rocznik
Tom
Strony
137--146
Opis fizyczny
Bibliogr. 10 poz.
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autor
- Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan, aichi@math.tsukuba.ac.jp
Bibliografia
- [1] M. Bestvina, Characterizing k-dimensional universal Monger compacta, Mem. Amer. Math. Soc. 380 (1988).
- [2] M. Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 10 (1960), 478-483.
- [3] H. Kato and E. Matsuhashi, On surjective Bing maps. Bull. Polish Acad. Sci. Math. 52 (2004), 329-333.
- [4] J. Krasinkiewicz, On mappings with hereditarily indecomposable fibers, ibid. 44 (1996), 147-156.
- [5] —, On approximation of mappings into 1-manifolds, ibid. 44 (1996), 431-440.
- [6] M. Levin, Bing maps and finite-dimensional maps, Fund. Math. 151 (1996). 47-52.
- [7] —, Certain finite dimensional maps and their application to hyperspaces, Israel J. Math. 105 (1998), 257-262.
- [8] M. Levin and W. Lewis, Some mapping theorems for extensional dimension, ibid. 133 (2003), 61-76.
- [9] J. van Mill, Infinite-Dimensional Topology. Prerequisites and Introduction, North-Holland, 1989.
- [10] J. Song and E. D. Tymchatyn, Free spaces, Fund. Math. 163 (2000), 229-239.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BAT5-0011-0023