Countably compact, locally countable 𝑇₂-spaces

Vaughan, J. E.

doi:10.1090/S0002-9939-1980-0574525-X

Countably compact, locally countable $T_{2}$-spaces
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Proc. Amer. Math. Soc. 80 (1980), 147-153 Request permission

Abstract:

The results of this paper provide a simple method for constructing locally countable ${T_2}$-spaces (not ${T_3}$) in which every infinite closed set has cardinality ${2^c}$. The spaces are used in a variety of ways as counterexamples. One of these spaces may be considered as a countably compact version of the Katětov H-closed extension of the natural numbers.

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