Continuous and proper decompositions
HTML articles powered by AMS MathViewer
- by G. K. Williams PDF
- Proc. Amer. Math. Soc. 28 (1971), 267-270 Request permission
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
-
P. Alexandroff and H. Hopf, Topologie. Vol. I, Springer, Berlin, 1935.
- Henri Cartan, Quotients of complex analytic spaces, Contributions to function theory (Internat. Colloq. Function Theory, Bombay, 1960) Tata Institute of Fundamental Research, Bombay, 1960, pp. 1–15. MR 0139769
- Jürgen Flachsmeyer, Über halbstetige Zerlegungen topologischer Räume, Math. Nachr. 24 (1962), 1–12 (German). MR 148024, DOI 10.1002/mana.19620240102
- Harald Holmann, Komplexe Räume mit komplexen Transformations-gruppen, Math. Ann. 150 (1963), 327–360 (German). MR 150789, DOI 10.1007/BF01470762
- Ingo Lieb, Über komplexe Räume and komplexe Spektren, Invent. Math. 1 (1966), 45–58 (German). MR 197776, DOI 10.1007/BF01389698
- R. L. Moore, Foundations of point set theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR 0150722
- Karl Stein, Analytische Zerlegungen komplexer Räume, Math. Ann. 132 (1956), 63–93 (German). MR 83045, DOI 10.1007/BF01343331
- A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690–700. MR 87078, DOI 10.1090/S0002-9939-1956-0087078-6
- G. T. Whyburn, Continuous decompositions, Amer. J. Math. 71 (1949), 218–226. MR 27507, DOI 10.2307/2372107
- G. T. Whyburn, Open mappings on locally compact spaces, Mem. Amer. Math. Soc. 1 (1950), i+24. MR 46641
Additional Information
- © Copyright 1971 American Mathematical Society
- 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