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, T2, locally countable, first countable, hereditarily separable, sequentially compact non-compact space X. The one point compactification X* of X is a compact, T2, C-space (meaning X* is of countable tightness) which is not sequential. We also construct a compact, T2, 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.
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Reference
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.
V.V. Fedorchuk, "On the cardinality of hereditarily separable compact Hausdorff spaces", Soviet. Math. Dokl 16 (1975), 651–655.
S.P. Franklin and M. Rajagopalan, "Some examples in topology", Trans. Amer. Math. Soc. 155 (1971), 305–314.
I. Juhasz, "Cardinal Functions in Topology", Mathematical Centre Tracts, Amsterdam, 1971.
V. Kannan, "Studies in Topology", Thesis, Madurai University, Madurai (INDIA), 1970.
R.C. Moore and G.S. Mrowka, "Topologies determined by countable objects", Notices of Amer. Math. Soc. 11 (1964), 554.
A. Ostazewski, "On countably compact perfectly normal spaces", J. Lond. Math. Soc., (to appear).
T.C. Pryzymusinski, "A Lindelöf space X such that X2 is normal, but not paracompact", Fund. Math. 78 (1973) 291–296.
M. Rajagopalan, "Scattered spaces III", to appear in J. Ind. Math. Soc.
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.
M.E. Rudin, "Lecture notes in set theoretic topology", CBMS Lecture series, American Mathematical Society, Providence (R.I.) 1975.
R. Vaidyanathaswamy, "Set theoretic topology", Chelsea, New York (1960).
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Rajagopalan, M. (1977). Compact C-spaces and S-spaces. In: Novák, J. (eds) General Topology and Its Relations to Modern Analysis and Algebra IV. Lecture Notes in Mathematics, vol 609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068682
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DOI: https://doi.org/10.1007/BFb0068682
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