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Everywhere Nonrecursive r.e. Sets in Recursively Presented Topological Spaces

Part of: Computability and recursion theory Generalities

Published online by Cambridge University Press:  09 April 2009

Li Xiang
Li Xiang
Affiliation:
Department of Mathematics Guizhou UniversityGuiyang People's Republic of China
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Abstract

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Recursively presented topological spaces are topological spaces with a recursive system of basic neighbourhoods. A recursively enumerable (r.e.) open set is a r.e. union of basic neighbourhoods. A set is everywhere r.e. open if its intersection with each basic neighbourhood is r.e. Similarly we define everywhere creative, everywhere simple, everywhere r.e. non-recursive sets and show that there exist sets both with and without these everywhere properties.

MSC classification

Secondary: 03D45: Theory of numerations, effectively presented structures 54A05: Topological spaces and generalizations (closure spaces, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 1 , February 1988 , pp. 105 - 128
Copyright
Copyright © Australian Mathematical Society 1988

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