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: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},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2005/137},
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 |
