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1996 | 149 | 3 | 265-274
Tytuł artykułu

A dimension raising hereditary shape equivalence

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We construct a hereditary shape equivalence that raises transfinite inductive dimension from ω to ω+1. This shows that ind and Ind do not admit a geometric characterisation in the spirit of Alexandroff's Essential Mapping Theorem, answering a question asked by R. Pol.
Słowa kluczowe
Rocznik
Tom
149
Numer
3
Strony
265-274
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-05-09
Twórcy
  • Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35487-0350, U.S.A., jdijkstr@ua1vm.ua.edu
Bibliografia
  • [1] P. S. Alexandroff, Dimensionstheorie. Ein Beitrag zur Geometrie der abgeschlossenen Mengen, Math. Ann. 106 (1932), 161-238.
  • [2] F. D. Ancel, The role of countable dimensionality in the theory of cell-like relations, Trans. Amer. Math. Soc. 287 (1985), 1-40.
  • [3] F. D. Ancel, Proper hereditary shape equivalences preserve Property C, Topology Appl. 19 (1985), 71-74.
  • [4] P. Borst, Transfinite classifications of weakly infinite-dimensional spaces, Free University Press, Amsterdam, 1986.
  • [5] P. Borst and J. J. Dijkstra, Essential mappings and transfinite dimension, Fund. Math. 125 (1985), 41-45.
  • [6] J. J. Dijkstra, J. van Mill, and J. Mogilski, An AR-map whose range is more infinite-dimensional than its domain, Proc. Amer. Math. Soc. 114 (1992), 279-285.
  • [7] J. J. Dijkstra and J. Mogilski, A geometric approach to the dimension theory of infinite-dimensional spaces, in: Proc. 8th Ann. Workshop Geom. Topology, Univ. of Wisconsin-Milwaukee, 1991, 59-63.
  • [8] T. Dobrowolski and L. Rubin, The hyperspaces of infinite-dimensional compacta for covering and cohomological dimension are homeomorphic, Pacific J. Math. 164 (1994), 15-39.
  • [9] A. N. Dranišnikov [A. N. Dranishnikov], On a problem of P. S. Alexandrov, Mat. Sb. 135 (1988), 551-557 (in Russian).
  • [10] R. Engelking, Dimension Theory, North-Holland, Amsterdam, 1978.
  • [11] R. Geoghegan and R. R. Summerhill, Pseudo-boundaries and pseudo-interiors in euclidean spaces and topological manifolds, Trans. Amer. Math. Soc. 194 (1974), 141-165.
  • [12] W. E. Haver, Mappings between ANR's that are fine homotopy equivalences, Pacific J. Math. 58 (1975), 457-461.
  • [13] D. W. Henderson, A lower bound for transfinite dimension, Fund. Math. 64 (1968), 167-173.
  • [14] W. Hurewicz, Ueber unendlich-dimensionale Punktmengen, Proc. Akad. Amsterdam 31 (1928), 916-922.
  • [15] G. Kozlowski, Images of ANR's, unpublished manuscript.
  • [16] J. van Mill and J. Mogilski, Property C and fine homotopy equivalences, Proc. Amer. Math. Soc. 90 (1984), 118-120.
  • [17] R. Pol, On a classification of weakly infinite-dimensional compacta, Topology Proc. 5 (1980), 231-242.
  • [18] R. Pol, On classification of weakly infinite-dimensional compacta, Fund. Math. 116 (1983), 169-188.
  • [19] Ju. M. Smirnov, On universal spaces for certain classes of infinite dimensional spaces, Amer. Math. Soc. Transl. Ser. 2, 21 (1962), 21-33.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv149i3p265bwm
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