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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Countable size nonmetrizable spaces which are stratifiable and $ \kappa$-metrizable


Author: Masami Sakai
Journal: Proc. Amer. Math. Soc. 122 (1994), 265-273
MSC: Primary 54D15; Secondary 54E20, 54E35
MathSciNet review: 1231043
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1231043-3
PII: S 0002-9939(1994)1231043-3
Keywords: Monotonically normal space, stratifiable space, $ \kappa $-metrizable space, w-space, bisequential, the Cantor tree, fan tightness
Article copyright: © Copyright 1994 American Mathematical Society