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)



Total paracompactness of real GO-spaces

Authors: Zoltán T. Balogh and Harold Bennett
Journal: Proc. Amer. Math. Soc. 101 (1987), 753-760
MSC: Primary 54F05; Secondary 54D18
MathSciNet review: 911046
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • [BL$ _{1}$] H. R. Bennett and D. J. Lutzer, eds., Topology and ordered structures, Part 1, Mathematical Centre Tracts No. 142, Amsterdam, 1981.
  • [BL$ _{2}$] H. R. Bennett and D. J. Lutzer, eds., Topology and ordered structures, Part 2, Mathematical Centre Tracts No. 169, Amsterdam, 1983. MR 736689 (85h:54053)
  • [Fa] M. F. Faber, Metrizability in generalized ordered spaces, Mathematical Centre Tracts No. 53, Amsterdam, 1974. MR 0418053 (54:6097)
  • [Fo] R. M. Ford, Basis properties in dimension theory, Doctoral Dissertation, Auburn University, Auburn, Ala., 1963.
  • [H] R. W. Heath, Screenability, pointwise paracompactness, and metrization of Moore spaces, Canad. J. Math. 16 (1964), 763-770. MR 0166760 (29:4033)
  • [Le] A. Lelek, Mathematical Problem Book, Univ. of Houston, Problem No. 99.
  • [Lu] D. J. Lutzer, On generalized ordered spaces, Dissertationes Math. 89 (1971). MR 0324668 (48:3018)
  • [M] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 61 (1963), 375-376. MR 0152985 (27:2956)
  • [OF$ _{1}$] J. M. O'Farrell, The Sorgenfrey Line is not totally metacompact, Houston J. Math 9 (1983), 271-273. MR 703275 (84i:54039)
  • [OF$ _{2}$] J. M. O'Farrell, Some results concerning the Hurewicz property, Fund. Math. (to appear).
  • [S] R. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947). MR 0020770 (8:594f)
  • [T] R. Telgarsky, Total paracompactness and paracompact dispersed spaces, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. 16 (1968), 567-572. MR 0235517 (38:3826)
  • [TK] R. Telgarsky and H. Kok, The space of rationals is not absolutely paracompact, Fund. Math. 73 (1971), 75-78. MR 0293585 (45:2662)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F05, 54D18

Retrieve articles in all journals with MSC: 54F05, 54D18

Additional Information

Keywords: Real GO-space, totally paracompact, totally metacompact, dense and codense example, metrizable
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society