Abstract
It is proved that in a T 3 space countable closed sets have countable character if and only if the set of limit point of the space is a countable compact set and every compact set is of countable character. Also, it is shown that spaces where countable sets have countable character are WN-spaces and are very close to M-spaces. Finally, some questions of Dai and Lia are discussed and some questions are proposed.
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References
A. V. Arhangelskii, Bicompact sets and the topology of spaces, Tran. Moscow Math. Soc., (1965), 1–62.
C. E. Aull, Closed set countability axioms, Indag. Math., 28 (1966), 311–316.
G. Beer, Spaces revisited, Amer. Math. Monthly, 95 (1988), 737–739.
Mumin Dai and Chuan Liu, Spaces in which Lindelöf closed sets have countable local base, Q and A in Gen. Top., 10 (1992), 1–7.
R. Sabella, Spaces in which compact subsets have countable local base, Proc. Amer. Math. Soc., 49 (1976), 499–504.
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Pareek, C.M. Spaces in Which Countable Closed Sets Have Countable Character. Acta Mathematica Hungarica 89, 253–257 (2000). https://doi.org/10.1023/A:1010616126746
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DOI: https://doi.org/10.1023/A:1010616126746