# Compact C-spaces and S-spaces

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## Abstract

We introduce a set theoretic axiom which is weaker than as well as axiom F. Using (CH) and we prove the existence of a locally compact, T

_{2}, locally countable, first countable, hereditarily separable, sequentially compact non-compact space X. The one point compactification X* of X is a compact, T_{2}, C-space (meaning X* is of countable tightness) which is not sequential. We also construct a compact, T_{2}, C-space Y which is not sequential using only the continuum hypothesis (CH). This solves some well known problems on S-spaces and also on compact C-spaces under least set theoretic axioms.## Preview

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## Reference

- (1).A.V. Arhangelskii, "On cardinal invariants, General Topology and its relation to Modern Algebra and Analysis III", Proceedings of third Prague Topology Symposium (1971), 37–46.Google Scholar
- (2).V.V. Fedorchuk, "On the cardinality of hereditarily separable compact Hausdorff spaces", Soviet. Math. Dokl 16 (1975), 651–655.MATHGoogle Scholar
- (3).S.P. Franklin and M. Rajagopalan, "Some examples in topology", Trans. Amer. Math. Soc. 155 (1971), 305–314.MathSciNetCrossRefMATHGoogle Scholar
- (4).I. Juhasz, "Cardinal Functions in Topology", Mathematical Centre Tracts, Amsterdam, 1971.MATHGoogle Scholar
- (5).V. Kannan, "Studies in Topology", Thesis, Madurai University, Madurai (INDIA), 1970.Google Scholar
- (6).R.C. Moore and G.S. Mrowka, "Topologies determined by countable objects", Notices of Amer. Math. Soc. 11 (1964), 554.Google Scholar
- (7).A. Ostazewski, "On countably compact perfectly normal spaces", J. Lond. Math. Soc., (to appear).Google Scholar
- (8).T.C. Pryzymusinski, "A Lindelöf space X such that X
^{2}is normal, but not paracompact", Fund. Math. 78 (1973) 291–296.MathSciNetGoogle Scholar - (9).M. Rajagopalan, "Scattered spaces III", to appear in J. Ind. Math. Soc.Google Scholar
- (10).M. Rajagopalan, "Some outstanding problems in topology and the V-process", Categorical Topology, Mannheim (1975), Lecture notes in mathematics, Vol. 540, Springer-Verlag, Berlin, (1976) 500–517.MATHGoogle Scholar
- (11).M.E. Rudin, "Lecture notes in set theoretic topology", CBMS Lecture series, American Mathematical Society, Providence (R.I.) 1975.Google Scholar
- (12).R. Vaidyanathaswamy, "Set theoretic topology", Chelsea, New York (1960).Google Scholar

## Copyright information

© Springer-Verlag 1977