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arXiv · 1305.3393

Every Separable Metrizable Space has a Proper Dyadic Subbase

Haruto Ohta·Hideki Tsuiki·Kohzo Yamada
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Abstract

The notions of a proper dyadic subbase and an independent subbase was introduced by H. Tsuiki to investigate in {0, 1, bot}-sequence codings of topological spaces. We show that every separable metrizable space has a proper dyadic subbase whose restriction to the perfect set defined by the Cantor-Bendixson theorem forms an independent subbase of the restricted space.

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Haruto Ohta, Hideki Tsuiki, Kohzo Yamada. 2013-05-15. Every Separable Metrizable Space has a Proper Dyadic Subbase. https://arxiv.org/abs/1305.3393

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