Countable size nonmetrizable spaces which are stratifiable and 𝜅-metrizable

Sakai, Masami

doi:10.1090/S0002-9939-1994-1231043-3

Countable size nonmetrizable spaces which are stratifiable and $\kappa$-metrizable
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Proc. Amer. Math. Soc. 122 (1994), 265-273 Request permission

Abstract:

K. Tamano asked the following question. Is a stratifiable space metrizable if it is $\kappa$-metrizable? To answer this question, we show that the class of stratifiable $\kappa$-metrizable spaces is much wider than that of metrizable spaces. In fact, we describe two very distinct classes of countable, stratifiable $\kappa$-metrizable spaces which are not metrizable. One of them has no nontrivial convergent sequence. The other is bisequential but not a w-space. In addition, we give a characterization of $\kappa$-metrizability of countable spaces defined by the Cantor tree and note a topological property of monotonically normal $\kappa$-metrizable spaces.

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