Towards Computability over Effectively Enumerable Topological Spaces

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Abstract

In this paper we study different approaches to computability over effectively enumerable topological spaces. We introduce and investigate the notions of computable function, strongly-computable function and weakly-computable function. Under natural assumptions on effectively enumerable topological spaces the notions of computability and weakly-computability coincide.

Keywords

Computably enumerable topological space
computability
effective continuity

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This research was partially supported by CICADA project, RFBR 070100543-a and RFBR-DFG Project GZ: 436 RUS 113/850/01:06-01-04002.