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1995 | 147 | 1 | 39-59
Tytuł artykułu

The minimum uniform compactification of a metric space

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that associated with each metric space (X,d) there is a compactification $u_dX$ of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of $u_dX$ are presented, and a detailed study of the structure of $u_dX$ is undertaken. This culminates in a topological characterization of the outgrowth $u_dℝ^n ∖ ℝ^n$, where $(ℝ^n,d)$ is Euclidean n-space with its usual metric.
Słowa kluczowe
Rocznik
Tom
147
Numer
1
Strony
39-59
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-02-15
poprawiono
1994-08-31
poprawiono
1994-12-02
Twórcy
  • Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Bibliografia
  • [A] M. Atsuji, Uniform continuity of continuous functions of metric spaces, Pacific J. Math. 8 (1958), 1-16.
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  • [vD] E. K. van Douwen, Remote points, Dissertationes Math. 188 (1981).
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  • [HY] J. Hocking and G. Young, Topology, Addison-Wesley, Reading, 1961.
  • [K] M. Katětov, On real-valued functions in topological spaces, Fund. Math. 38 (1951), 85-91.
  • [LR] R. Levy and M. D. Rice, Techniques and examples in U-embedding, Topology Appl. 22 (1986), 157-174.
  • [Ma] K. D. Magill, Jr., The lattice of compactifications of a locally compact space, Proc. London Math. Soc. (3) 18 (1968), 231-244.
  • [M] D. Mattson, Discrete subsets of proximity spaces, Canad. J. Math. 31 (1979), 225-230.
  • [NW] S. Naimpally and B. Warrack, Proximity Spaces, Cambridge Univ. Press, 1970.
  • [PW] J. R. Porter and R. G. Woods, Extensions and Absolutes of Hausdorff Spaces, Springer, 1987.
  • [R] M. C. Rayburn, Proximities, unpublished manuscript.
  • [Ra] J. Rainwater, Spaces whose finest uniformity is metric, Pacific J. Math. 9 (1959), 567-570.
  • [S] Yu. M. Smirnov, Mappings of systems of open sets, Mat. Sb. (73) 31 (1952), 152-166 (in Russian).
  • [Wa] R. C. Walker, The Stone-Čech Compactification, Springer, New York, 1974.
  • [Wi] S. Willard, General Topology, Addison-Wesley, Reading, 1970.
  • [Wo1] R. G. Woods, Certain properties of βX - X for σ-compact X, doctoral dissertation, McGill Univ., Montreal, 1969.
  • [Wo2] R. G. Woods, Coabsolutes of remainders of Stone-Čech compactifications, Pacific J. Math. 37 (1971), 545-560.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv147i1p39bwm
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