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Proceedings of the American Mathematical Society

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Quotients of proximity spaces


Author: Louis Friedler
Journal: Proc. Amer. Math. Soc. 37 (1973), 589-594
MSC: Primary 54E05; Secondary 54C10
MathSciNet review: 0402691
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Abstract: A characterization of the quotient proximity is given. It is used to find necessary and sufficient conditions for every proximity map on a space to be a topological quotient map. It is shown that a separated proximity space is compact iff every p-map on X with separated range is a proximity quotient map.


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  • [1] C. H. Dowker, Mappings of proximity structures, General Topology and its Relations to Modern Analysis and Algebra (Proc. Sympos., Prague, 1961) Academic Press, New York; Publ. House Czech. Acad. Sci., Prague, 1962, pp. 139–141. MR 0146792
  • [2] J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323
  • [3] Miroslav Katětov, Über die Berührungsräume, Wiss. Z. Humboldt-Univ. Berlin Math.-Natur. Reihe 9 (1959/1960), 685–691 (German, with Russian, English, and French summaries). MR 0184199
  • [4] S. Leader, On clusters in proximity spaces, Fund. Math. 47 (1959), 205–213. MR 0112120
  • [5] S. MacDonald and S. Willard, Domains of paracompactness and regularity, Canad. J. Math. 24 (1972), 1079–1085. MR 0313993
  • [6] L. J. Nachman, Quotients of complete proximity spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 17–20 (English, with Loose Russian summary). MR 0266150
  • [7] V. Z. Poljakov, Open mappings of proximity spaces, Dokl. Akad. Nauk SSSR 155 (1964), 1014–1017 (Russian). MR 0172240
  • [8] V. Z. Poljakov, Proximally open mappings of metric spaces, Dokl. Akad. Nauk SSSR 186 (1969), 1012–1015 (Russian). MR 0253278
  • [9] A. H. Stone, Lecture notes, University of Rochester, Rochester, N.Y., 1967 (unpublished).
  • [10] Stephen Willard, General topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0264581

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0402691-1
Keywords: Quotient map, p-quotient map, p-open map
Article copyright: © Copyright 1973 American Mathematical Society