Every Separable Metrizable Space has a Proper Dyadic Subbase
General Topology
2013-05-16 v1
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.
Cite
@article{arxiv.1305.3393,
title = {Every Separable Metrizable Space has a Proper Dyadic Subbase},
author = {Haruto Ohta and Hideki Tsuiki and Kohzo Yamada},
journal= {arXiv preprint arXiv:1305.3393},
year = {2013}
}