Yasuyuki Tsukamoto - Existence of strongly proper dyadic subbases

lmcs:3198 - Logical Methods in Computer Science, March 30, 2017, Volume 13, Issue 1 - https://doi.org/10.23638/LMCS-13(1:18)2017
Existence of strongly proper dyadic subbases

Authors: Yasuyuki Tsukamoto

    We consider a topological space with its subbase which induces a coding for each point. Every second-countable Hausdorff space has a subbase that is the union of countably many pairs of disjoint open subsets. A dyadic subbase is such a subbase with a fixed enumeration. If a dyadic subbase is given, then we obtain a domain representation of the given space. The properness and the strong properness of dyadic subbases have been studied, and it is known that every strongly proper dyadic subbase induces an admissible domain representation regardless of its enumeration. We show that every locally compact separable metric space has a strongly proper dyadic subbase.


    Volume: Volume 13, Issue 1
    Published on: March 30, 2017
    Accepted on: March 30, 2017
    Submitted on: March 30, 2017
    Keywords: Mathematics - General Topology,I.1.1,F.3.2,F.4.1

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