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URN: urn:nbn:de:0030-drops-1376
URL: http://drops.dagstuhl.de/opus/volltexte/2005/137/
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### Dyadic Subbases and Representations of Topological Spaces

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### 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:DSP:2005:137,
author =	{Hideki Tsuiki},
title =	{Dyadic Subbases and Representations of Topological Spaces},
booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
year =	{2005},
editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
number =	{04351},
series =	{Dagstuhl Seminar Proceedings},
ISSN =	{1862-4405},
publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
annote =	{Keywords: Dyadic subbase , embedding , computation over topological spaces , Plotkin's $T^\omega$}

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