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