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  1. Effective Inseparability in a Topological Setting.Dieter Spreen - 1996 - Annals of Pure and Applied Logic 80 (3):257-275.
    Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively enumerable set, if X (...)
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  • Point-Free Topological Spaces, Functions and Recursive Points; Filter Foundation for Recursive Analysis. I.Iraj Kalantari & Lawrence Welch - 1998 - Annals of Pure and Applied Logic 93 (1-3):125-151.
    In this paper we develop a point-free approach to the study of topological spaces and functions on them, establish platforms for both and present some findings on recursive points. In the first sections of the paper, we obtain conditions under which our approach leads to the generation of ideal objects with which mathematicians work. Next, we apply the effective version of our approach to the real numbers, and make exact connections to the classical approach to recursive reals. In the succeeding (...)
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  • Effective Topological Spaces I: A Definability Theory.Iraj Kalantari & Galen Weitkamp - 1982 - Annals of Pure and Applied Logic 29 (1):1-27.
  • Effective Topological Spaces III: Forcing and Definability.Iraj Kalantari & Galen Weitkamp - 1987 - Annals of Pure and Applied Logic 36 (1):17-27.