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2000 | 163 | 3 | 241-265
Tytuł artykułu

Does C* -embedding imply C*-embedding in the realm of products with a non-discrete metric factor?

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.
Słowa kluczowe
Rocznik
Tom
163
Numer
3
Strony
241-265
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-27
poprawiono
1999-12-08
Twórcy
  • School of Mathematical and Statistical Sciences, Faculty of Science, University of Natal, King George V Avenue, Durban 4041, South Africa, gutev@sci.und.ac.za
autor
Bibliografia
  • [1] R. A. Aló and L. I. Sennott, Extending linear space-valued functions, Math. Ann. 191 (1971), 79-86.
  • [2] R. A. Aló and L. I. Sennott, Collectionwise normality and the extension of functions on product spaces, Fund. Math. 74 (1972), 231-243.
  • [3] R. Arens, Extension of coverings, of pseudometrics, and linear-space-valued mappings, Canad. J. Math. 5 (1953), 211-215.
  • [4] R. L. Blair and A. W. Hager, Extensions of zero-sets and of real-valued functions, Math. Z. 136 (1974), 41-52.
  • [5] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367.
  • [6] T. E. Gantner, Extension of uniformly continuous pseudometrics, Trans. Amer. Math. Soc. 132 (1968), 147-157.
  • [7] G. Gruenhage, Generalized metric spaces, in: Handbook of Set-Theoretic Topo- logy, K. Kunen and J. E. Vaughan (eds.), North-Holland, Amsterdam, 1984, 423-501.
  • [8] T. Hoshina, Spaces with a property related to uniformly local finiteness, Tsukuba J. Math. 6 (1982), 51-62.
  • [9] T. Hoshina, Extensions of mappings II, in: Topics in General Topology, K. Morita and J. Nagata (eds.), North-Holland, Amsterdam, 1989, 41-80.
  • [10] T. Hoshina, Extensions of mappings, in: Recent Progress in General Topology, M. Hušek and J. van Mill (eds.), North-Holland, Amsterdam, 1992, 405-416.
  • [11] T. Hoshina and K. Yamazaki, C*-embedding and C-embedding on products with certain metric factor, Topology Appl. 82 (1998), 195-204.
  • [12] J. R. Isbell, Uniform Spaces, Amer. Math. Soc., Providence, RI, 1964.
  • [13] T. Ishii and H. Ohta, Generalizations of C-embedding and their applications, Math. Japon. 23 (1978), 349-368.
  • [14] F. Ishikawa, On countably paracompact spaces, Proc. Japan Acad. 31 (1955), 686-687.
  • [15] M. Katětov, Extensions of locally finite coverings, Colloq. Math. 6 (1958), 145-151.
  • [16] K. Kunen, Set Theory. An Introduction to Independence Proofs, Stud. Logic Found. Math. 102, North-Holland, Amsterdam, 1983.
  • [17] K. Morita, Paracompactness and product spaces, Fund. Math. 50 (1962), 223-236.
  • [18] K. Morita, Products of normal spaces with metric spaces, Math. Ann. 154 (1964), 365-382.
  • [19] K. Morita, On generalizations of Borsuk's homotopy extension theorem, Fund. Math. 88 (1975), 1-6.
  • [20] K. Morita and T. Hoshina, P-embedding and product spaces, ibid. 93 (1976), 71-80.
  • [21] H. Ohta, Rectangular normality of products with a metric factor, RIMS Kôkyûroku 823 (1993), 106-117.
  • [22] T. C. Przymusiński, Collectionwise normality and extensions of continuous functions, Fund. Math. 98 (1978), 75-81.
  • [23] T. C. Przymusiński, Extending functions from products with a metric factor and absolutes, Pacific J. Math. 101 (1982), 463-475.
  • [24] T. C. Przymusiński, Notes on extendability of continuous functions from products with a metric factor, unpublished note, May 1983.
  • [25] T. C. Przymusiński, A solution to a problem of E. Michael, Pacific J. Math. 114 (1984), 235-242.
  • [26] T. C. Przymusiński and M. Wage, Collectionwise normality and extensions of locally finite coverings, Fund. Math. 109 (1980), 175-187.
  • [27] M. E. Rudin and M. Starbird, Products with a metric factor, General Topology Appl. 5 (1975), 235-248.
  • [28] H. L. Shapiro, Extensions of pseudometrics, Canad. J. Math 18 (1966), 981-998.
  • [29] M. Starbird, Extending maps from products, in: Studies in Topology, N. H. Stav- rakas and K. R. Allen (eds.), Academic Press, New York, 1975, 559-564.
  • [30] K. Yamazaki, C*-embedding and C-embedding on product spaces, Tsukuba J. Math. 21 (1997), 515-527.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv163i3p241bwm
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