Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Continuous and proper decompositions


Author: G. K. Williams
Journal: Proc. Amer. Math. Soc. 28 (1971), 267-270
MSC: Primary 54.60
DOI: https://doi.org/10.1090/S0002-9939-1971-0273583-4
MathSciNet review: 0273583
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If $ X$ is a locally connected, locally peripherally compact Hausdorff space and if $ R$ is an equivalence relation on $ X$ with fibers which are connected with compact boundaries, then it is shown that three definitions of continuity of $ R$ are equivalent. Some of the propositions used to obtain this result are then applied to get sufficient conditions for a decomposition of certain types of metric spaces to be proper.


References [Enhancements On Off] (What's this?)

  • [1] P. Alexandroff and H. Hopf, Topologie. Vol. I, Springer, Berlin, 1935.
  • [2] H. Cartan, Quotients of analytic spaces, Internat. Colloq. Contribution to Function Theory (Bombay, 1960), Tata Institute of Fundamental Research, Bombay, 1960, pp. 1-15. MR 25 #3199. MR 0139769 (25:3199)
  • [3] J. Flachsmeyer, Über halbstetige Zerlegungen topologischer Räume, Math. Nachr. 24 (1962), 1-12. MR 26 #5534. MR 0148024 (26:5534)
  • [4] H. Holmann, Komplexe Räume mit komplexen Transformationsgruppen, Math. Ann. 150 (1963), 327-360. MR 27 #776. MR 0150789 (27:776)
  • [5] I. Lieb, Über komplexe Räume und komplexe Spektren, Invent. Math. 1 (1966), 45-58. MR 33 #5939. MR 0197776 (33:5939)
  • [6] R. L. Moore, Foundations of point set theory, Amer. Math. Soc. Colloq. Publ., vol. 13, Amer. Math. Soc., Providence, R. I., 1932. MR 0150722 (27:709)
  • [7] K. Stein, Analytische Zerlegung komplexer Räume, Math. Ann. 132 (1956), 63-93. MR 18, 649. MR 0083045 (18:649c)
  • [8] A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690-700. MR 19, 299. MR 0087078 (19:299b)
  • [9] G. T. Whyburn, Continuous decompositions, Amer. J. Math. 71 (1949), 218-226. MR 10, 317. MR 0027507 (10:317b)
  • [10] -, Open mappings on locally compact spaces, Mem. Amer. Math. Soc. No. 1 (1950). MR 13, 764. MR 0046641 (13:764j)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.60

Retrieve articles in all journals with MSC: 54.60


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0273583-4
Keywords: Semicontinuous decompositions, continuous decompositions, proper decompositions, open equivalence relation, closed equivalence relation, semiclosed equivalence relation, locally peripherally compact space
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society