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1994 | 144 | 2 | 95-117
Tytuł artykułu

Ordinal products of topological spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of the ordinal product of a transfinite sequence of topological spaces which is an extension of the finite product operation is introduced. The dimensions of finite and infinite ordinal products are estimated. In particular, the dimensions of ordinary products of Smirnov's [S] and Henderson's [He1] compacta are calculated.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
144
Numer
2
Strony
95-117
Opis fizyczny
Daty
wydano
1994
otrzymano
1992-05-19
poprawiono
1993-02-09
poprawiono
1993-05-20
Twórcy
Bibliografia
  • [A-Pa] P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory, Nauka, Moscow, 1973 (in Russian).
  • [B1] P. Borst, Classification of weakly infinite-dimensional spaces. Part I: A transfinite extension of the covering dimension, Fund. Math. 130 (1988), 1-25.
  • [B2] P. Borst, Classification of weakly infinite-dimensional spaces. Part II: Essential mappings, ibid., 73-99.
  • [B3] P. Borst, Some remarks concerning C-spaces, preprint.
  • [D] A. N. Dranishnikov, Absolute extensors in dimension n and dimension raising n-soft mappings, Uspekhi Mat. Nauk 39 (5) (1984), 55-95 (in Russian).
  • [E1] R. Engelking, General Topology, PWN, Warszawa 1977.
  • [E2] R. Engelking, Dimension Theory, PWN, Warszawa 1978.
  • [E3] R. Engelking, Transfinite dimension, in: Surveys in General Topology, G. M. Reed (ed.), Academic Press, New York, 1980, 131-161.
  • [F] V. V. Filippov, On the inductive dimension of the product of bicompacta, Dokl. Akad. Nauk SSSR 202 (1972), 1016-1019 (in Russian).
  • [Ha] Y. Hattori, Solution of problems concerning transfinite dimension, Questions Answers Gen. Topology 1 (1983), 128-134.
  • [Ha-Y] Y. Hattori and K. Yamada, Closed pre-images of C-spaces, Math. Japon. 34 (1989), 555-561.
  • [H] F. Hausdorff, Set Theory, Chelsea, New York, 1962.
  • [He1] D. W. Henderson, A lower bound for transfinite dimension, Fund. Math. 63 (1968), 167-173.
  • [He2] D. W. Henderson, D-dimension I. A new transfinite dimension, Pacific J. Math. 26 (1968), 91-107.
  • [Hes] G. Hessenberg, Grundbegriffe der Mengenlehre, Göttingen, 1906.
  • [K-M] K. Kuratowski and A. Mostowski, Set Theory, PWN and North-Holland, 1976.
  • [Le] B. T. Levshenko, Spaces of transfinite dimensionality, Mat. Sb. 67 (1965), 255-266 (in Russian); English transl.: Amer. Math. Soc. Transl. (2) 73 (1968), 135-148.
  • [L] L. A. Luxemburg, On compacta with non-coinciding transfinite dimensions, Dokl. Akad. Nauk SSSR 212 (1973), 1297-1300 (in Russian); English transl.: Soviet Math. Dokl. 14 (1973), 1593-1597.
  • [Pa1] B. A. Pasynkov, On dimension of rectangular products, Dokl. Akad. Nauk SSSR 221 (1975), 291-294 (in Russian).
  • [Pa2] B. A. Pasynkov, On transfinite dimension, Abstracts of Leningrad Internat. Topology Conf., 1982 (in Russian).
  • [P] R. Pol, On classification of weakly infinite-dimensional compacta, Fund. Math. 116 (1983), 169-188.
  • [Po] L. Polkowski, On transfinite dimension, Colloq. Math. 50 (1985), 61-79.
  • [S] Yu. M. Smirnov, On universal spaces for some classes of infinite-dimensional spaces, Izv. Akad. Nauk SSSR 23 (1959), 185-196 (in Russian); English transl.: Amer. Math. Soc. Transl. (2) 21 (1962), 21-34.
  • [T] G. H. Toulmin, Shuffling ordinals and transfinite dimension, Proc. London Math. Soc. 4 (1954), 177-195.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv144i2p95bwm
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