J Austral Math Soc Ser A 44 pp105--128, 1988.

Everywhere Nonrecursive R.E Sets in Recursively Presented Topological Spaces

Li Xiang

Abstract

Recursively presented topological spaces are topological spaces with a recursive system of basic neighbouroods. 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.

1980 AMS Subject Classification: 03D45, 54A05

Browse the article

Authors

Li Xiang

Department of Mathematics, Guizhou University, Guiyang, People's Republic of China.