Total paracompactness of real GO-spaces
HTML articles powered by AMS MathViewer
- by Zoltán T. Balogh and Harold Bennett PDF
- Proc. Amer. Math. Soc. 101 (1987), 753-760 Request permission
Abstract:
A topological space is said to be totally paracompact (resp. totally metacompact) if every open base of it has a locally finite (resp. pointfinite) subcover. In this paper we characterize all totally paracompact GO-spaces constructed on the real line. It turns out that in the class of GO-spaces on the real line, total paracompactness and total metacompactness are equivalent. Another consequence of our characterization is that totally metacompact GO-spaces on the real line are metrizable. Questions and partial results are given concerning total paracompactness in subspaces of real GO-spaces.References
-
H. R. Bennett and D. J. Lutzer, eds., Topology and ordered structures, Part 1, Mathematical Centre Tracts No. 142, Amsterdam, 1981.
- H. Bennet and D. J. Lutzer, A note on perfect normality in generalized ordered spaces, Topology and order structures, Part 2 (Amsterdam, 1981) Math. Centre Tracts, vol. 169, Math. Centrum, Amsterdam, 1983, pp. 19–22. MR 736689
- M. J. Faber, Metrizability in generalized ordered spaces, Mathematical Centre Tracts, No. 53, Mathematisch Centrum, Amsterdam, 1974. MR 0418053 R. M. Ford, Basis properties in dimension theory, Doctoral Dissertation, Auburn University, Auburn, Ala., 1963.
- R. W. Heath, Screenability, pointwise paracompactness, and metrization of Moore spaces, Canadian J. Math. 16 (1964), 763–770. MR 166760, DOI 10.4153/CJM-1964-073-3 A. Lelek, Mathematical Problem Book, Univ. of Houston, Problem No. 99.
- D. J. Lutzer, On generalized ordered spaces, Dissertationes Math. (Rozprawy Mat.) 89 (1971), 32. MR 324668
- E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375–376. MR 152985, DOI 10.1090/S0002-9904-1963-10931-3
- J. M. O’Farrell, The Sorgenfrey line is not totally metacompact, Houston J. Math. 9 (1983), no. 2, 271–273. MR 703275 J. M. O’Farrell, Some results concerning the Hurewicz property, Fund. Math. (to appear).
- R. H. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), 631–632. MR 20770, DOI 10.1090/S0002-9904-1947-08858-3
- R. Telgársky, Total paracompactness and paracompact dispersed spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 567–572 (English, with Russian summary). MR 235517
- R. Telgársky and H. Kok, The space of rationals is not absolutely paracompact, Fund. Math. 73 (1971/72), no. 1, 75–78. MR 293585, DOI 10.4064/fm-73-1-75-78
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 753-760
- MSC: Primary 54F05; Secondary 54D18
- DOI: https://doi.org/10.1090/S0002-9939-1987-0911046-2
- MathSciNet review: 911046