caa a22 4500 388039752 CHVBK 20180307125017.0 cr unu---uuuuu 161130e199803 xx s 000 0 eng 10.2307/2586596 doi S0022481200015413 pii (NATIONALLICENCE)cambridge-10.2307/2586596 Spreen Dieter Fachbereich Mathematik, Theoretische Informatik, Universität-Gh Siegen, D-57068 Siegen, Germany, E-mail: spreen@informatik.uni-siegen.de On effective topological spaces [Elektronische Daten] [Dieter Spreen] Starting with D. Scott's work on the mathematical foundations of programming language semantics, interest in topology has grown up in theoretical computer science, under the slogan ‘open sets are semidecidable properties'. But whereas on effectively given Scott domains all such properties are also open, this is no longer true in general. In this paper a characterization of effectively given topological spaces is presented that says which semidecidable sets are open. This result has important consequences. Not only follows the classical Rice-Shapiro Theorem and its generalization to effectively given Scott domains, but also a recursion theoretic characterization of the canonical topology of effectively given metric spaces. Moreover, it implies some well known theorems on the effective continuity of effective operators such as P. Young and the author's general result which in its turn entails the theorems by Myhill-Shepherdson, Kreisel-Lacombe-Shoenfield and Ceĭtin-Moschovakis, and a result by Eršov and Berger which says that the hereditarily effective operations coincide with the hereditarily effective total continuous functionals on the natural numbers. Copyright © Association for Symbolic Logic 1998 The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 185-221 0022-4812 63:1<185 1998 63 JSL https://doi.org/10.2307/2586596 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586596 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Spreen Dieter Fachbereich Mathematik, Theoretische Informatik, Universität-Gh Siegen, D-57068 Siegen, Germany, E-mail: spreen@informatik.uni-siegen.de NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 185-221 0022-4812 63:1<185 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge