eng
episciences.org
Logical Methods in Computer Science
1860-5974
2017-03-30
Volume 13, Issue 1
10.23638/LMCS-13(1:18)2017
3198
journal article
Existence of strongly proper dyadic subbases
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.
https://lmcs.episciences.org/3198/pdf
Mathematics - General Topology
I.1.1
F.3.2
F.4.1