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)



Discrete subsets of perfectly normal spaces

Author: R. M. Stephenson
Journal: Proc. Amer. Math. Soc. 34 (1972), 605-608
MSC: Primary 54A25; Secondary 54B15
MathSciNet review: 0296885
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Following R. W. Heath and E. A. Michael [HM], we call a topological space perfect if each of its closed subsets is a $ {G_\delta }$.

In this note we (i) give a characterization of compact perfect $ {T_1}$ spaces and (ii) obtain some results concerning the cardinality of discrete subsets of perfect spaces.

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

  • [AU1] P. Alexan'drov and P. Urysohn, Mémoire sur les espaces topologiques compacts, Verh. Kon. Akad. Wetensch. Amsterdam 14 (1929), no. 1,1-96.
  • [AU2] -, ``On compact topological spaces,'' in P. S. Urysohn, Works in topology and other fields of mathematics. Vol. 2, G1TTL, Moscow, 1951. MR 14, 122.
  • [GJ] L. Gillman and M. Jerison, Rings of continuous functions, University Series in Higher Math., Van Nostrand, Princeton, N.J., 1960. MR 22 #6994. MR 0116199 (22:6994)
  • [GFW] S. L. Gulden, W. M. Fleischman and J. H. Weston, Linearly ordered topological spaces, Proc. Amer. Math. Soc. 24 (1970), 197-203: MR 40 #3511. MR 0250272 (40:3511)
  • [HJ] A. Hajnal and I. Juhász, Discrete subspaces of topological spaces, Nederl. Akad. Wetensch. Proc. Ser. A 70 = Indag. Math. 29 (1967), 343-356: MR 37 #4769. MR 0229195 (37:4769)
  • [HM] R. W. Heath and E. A. Michael, A property of the Sorgenfrey line, Compositio Math. 23 (1971), 185-188. MR 0287515 (44:4719)
  • [L] D. J. Lutzer, On generalized ordered spaces, Proc. Washington State Univ. Conf. on General Topology (Pullman, Wash., 1970), Pi Mu Epsilon, Dept. of Math., Washington State Univ., Pullman, Wash., 1970, pp. 102-110. MR 42 #1075. MR 0266167 (42:1075)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54A25, 54B15

Retrieve articles in all journals with MSC: 54A25, 54B15

Additional Information

Keywords: Compact perfectly normal spaces, discrete subspaces, countably compact perfect spaces
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society