License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.04351.15
URN: urn:nbn:de:0030-drops-1376
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2005/137/
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Tsuiki, Hideki

Dyadic Subbases and Representations of Topological Spaces

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04351.TsuikiHideki.Paper.137.pdf (0.1 MB)

Abstract

We explain topological properties of the embedding-based approach to
computability on topological spaces. With this approach, he considered
a special kind of embedding of a topological space into Plotkin's
$T^\omega$, which is the set of infinite sequences of $T = \{0,1,\bot \}$.
We show that such an embedding can also be characterized by a dyadic
subbase, which is a countable subbase $S = (S_0^0, S_0^1, S_1^0, S_1^1, \ldots)$ such that $S_n^j$ $(n = 0,1,2,\ldots; j = 0,1$ are regular open
and $S_n^0$ and $S_n^1$ are exteriors of each other. We survey properties
of dyadic subbases which are related to efficiency properties of the
representation corresponding to the embedding.

BibTeX - Entry

@InProceedings{tsuiki:DagSemProc.04351.15,
  author =	{Tsuiki, Hideki},
  title =	{{Dyadic Subbases and Representations of Topological Spaces}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--8},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2005/137},
  URN =		{urn:nbn:de:0030-drops-1376},
  doi =		{10.4230/DagSemProc.04351.15},
  annote =	{Keywords: Dyadic subbase , embedding , computation over topological spaces , Plotkin's \$T^\backslashomega\$}
}

Keywords: Dyadic subbase , embedding , computation over topological spaces , Plotkin's $T^\omega$
Collection: 04351 - Spatial Representation: Discrete vs. Continuous Computational Models
Issue Date: 2005
Date of publication: 22.04.2005

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