The Effectively Enumerable Topological Spaces

M. V. Korovina^a, O. V. Kudinov<sup>b

a</sup> A. P. Ershov Institute of Informatics Systems, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: In this paper we give a positive answer to the question proposed by Dana Scott on existence of a class of topological spaces which contains the computable metric spaces,the effective $\omega$-continuous domains as proper subclasses and for which computability coincides with effective continuity. In this paper we introduce and investigate the class of effectively enumerable topological spaces which satisfy these requirements.

UDC: 510.6+510.5

Received: 05.05.2008