Dyadic Subbases and Representations of Topological Spaces

Author Hideki Tsuiki

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Hideki Tsuiki

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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)


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


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