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1994 | 145 | 3 | 243-259
Tytuł artykułu

Classical-type characterizations of non-metrizable ANE(n)-spaces

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Abstrakty
EN
The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is $LC^{n-1} & C^{n-1}$ (resp., $LC^{n-1}$) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.
Twórcy
  • Institute of Mathematics with Computer Center, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 8, 1113 Sofia, Bulgaria, gutev@bgcict.bitnet
autor
  • Department of Mathematics, University of Sofia, 5 James Bourchier Blvd., 1126 Sofia, Bulgaria
Bibliografia
  • [1] A. Chigogidze, Noncompact absolute extensors in dimension n, n-soft mappings, and their applications, Izv. Akad. Nauk SSSR 50 (1) (1986), 156-180 (in Russian); English transl.: Math. USSR-Izv. 28 (1987), 151-174.
  • [2] A. Dranishnikov, Absolute extensors in dimension n and dimension-raising n-soft maps, Uspekhi Mat. Nauk 39 (5) (1984), 55-95 (in Russian); English transl.: Russian Math. Surveys 39 (1984).
  • [3] J. Dugundji, Absolute neighborhood retracts and local connectedness in arbitrary metric spaces, Compositio Math. 13 (1958), 229-246.
  • [4] V. Filippov, On the dimension of products of topological spaces, Fund. Math. 106 (1980), 181-212 (in Russian).
  • [5] V. Gutev, Selections for quasi-l.s.c. mappings with uniformly equi-$LC^n$ range, Set-Valued Anal. 1 (1993), 319-328.
  • [6] R. Haydon, On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim), Studia Math. 52 (1974), 23-31.
  • [7] K. Kuratowski, Sur les espaces localement connexes et péaniens en dimension n, Fund. Math. 24 (1935), 269-287.
  • [8] E. Michael, Continuous selections II, Ann. of Math. 64 (1956), 562-580.
  • [9] R. Pol and E. Puzio-Pol, Remarks on Cartesian products, Fund. Math. 93 (1976), 57-69.
  • [10] E. V. Ščepin [E. V. Shchepin], Functors and uncountable powers of compacta, Uspekhi Mat. Nauk 36 (3) (1981), 3-62 (in Russian); English transl.: Russian Math. Surveys 36 (1981).
  • [11] L. Shirokov, On AE(n)-compacta and n-soft mappings, Sibirsk. Mat. Zh. 33 (1992), 151-156 (in Russian).
  • [12] H. Toruńczyk, Concerning locally homotopy negligible sets and characterizations of $l_2$-manifolds, Fund. Math. 101 (1978), 93-110.
  • [13] V. Valov, Another characterization of AE(0)-spaces, Pacific J. Math. 127 (1987), 199-208.
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Bibliografia
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bwmeta1.element.bwnjournal-article-fmv145i3p243bwm
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