Dyadic Subbases and Representations of Topological Spaces

Tsuiki, Hideki

doi:10.4230/DagSemProc.04351.15

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Dyadic Subbases and Representations of Topological Spaces

Author Hideki Tsuiki

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 4351
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2005-04-22

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Document Identifiers

DOI: 10.4230/DagSemProc.04351.15
URN: urn:nbn:de:0030-drops-1376

Subject Classification

Keywords

Dyadic subbase
embedding
computation over topological spaces
Plotkin's $T^\omega$

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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.

Cite As Get BibTex

Hideki Tsuiki. Dyadic Subbases and Representations of Topological Spaces. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005) https://doi.org/10.4230/DagSemProc.04351.15

Author Details

Hideki Tsuiki

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