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)



On nowhere dense closed $ P$-sets

Authors: Kenneth Kunen, Jan van Mill and Charles F. Mills
Journal: Proc. Amer. Math. Soc. 78 (1980), 119-123
MSC: Primary 54D25; Secondary 54A25
MathSciNet review: 548097
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that no compact space of weight $ {\omega _1}$ can be covered by nowhere dense closed P-sets. In addition, we construct a compact space of weight $ {\omega _2}$ which can be covered by nowhere dense closed P-sets. As an application, we show that CH is equivalent to the statement that each small nonpseudocompact space has a remote point.

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

  • [vD] E. K. van Douwen, Remote points, Dissertationes Math. (to appear).
  • [vDvM] E. K. van Douwen and J. van Mill, Spaces without remote points (to appear).
  • [FG] N. J. Fine and L. Gillman, Remote points in $ \beta {\mathbf{R}}$, Proc. Amer. Math. Soc. 13 (1962), 29-36. MR 0143172 (26:732)
  • [GH] L. Gillman and M. Henriksen, Concerning rings of continuous functions, Trans. Amer. Math. Soc. 77 (1954), 340-362. MR 0063646 (16:156g)
  • [GJ] L. Gillman and M. Jerison, Rings of continuous functions, The University Series in Higher Mathematics, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
  • [vMM] J. van Mill and C. F. Mills, A topological property enjoyed by near points but not by large points (to appear). MR 572374 (81e:54024)
  • [W] R. G. Woods, Co-absolutes of remainders of Stone-Čech compactifications, Pacific J. Math. 37 (1971), 545-560. MR 0307179 (46:6300a)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D25, 54A25

Retrieve articles in all journals with MSC: 54D25, 54A25

Additional Information

Keywords: Nowhere dense, P-set, remote point, CH
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society