DagSemProc.04351.15.pdf
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Dyadic Subbases and Representations of Topological Spaces
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Dagstuhl Seminar Proceedings, Volume 4351
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
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- Publication Date: 2005-04-22
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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
https://doi.org/10.4230/DagSemProc.04351.15
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.
Keywords
- Dyadic subbase
- embedding
- computation over topological spaces
- Plotkin's $T^\omega$
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