Apartness spaces as a framework for constructive topology
نویسندگان
چکیده
An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed.
منابع مشابه
Apartness and formal topology
The theory of formal spaces and the more recent theory of apartness spaces have a priori not much more in common than that each of them was initiated as a constructive approach to general topology. We nonetheless try to do the first steps in relating these competing theories to each other. Formal topology was put forward in the mid 1980s by Sambin [8] in order to make available to Martin–Löf’s ...
متن کاملErik Palmgren and Peter Schuster
The theory of formal spaces and the more recent theory of apartness spaces have a priori not much more in common than that each of them was initiated as a constructive approach to general topology. We nonetheless try to do the first steps in relating these competing theories to each other. Formal topology was put forward in the mid 1980s by Sambin [11] in order to make available to Martin–Löf’s...
متن کاملContributions to Pointfree Topology and Apartness Spaces
Hedin, A. 2011. Contributions to Pointfree Topology and Apartness Spaces. Department of Mathematics. Uppsala Dissertations in Mathematics 71. 40 pp. Uppsala. The work in this thesis contains some contributions to constructive point-free topology and the theory of apartness spaces. The first two papers deal with constructive domain theory using formal topology. In Paper I we focus on the notion ...
متن کاملJourney into Apartness Space
On more than one occasion, the late Errett Bishop [1] suggested that general pointset topology might have little signi cance for constructive mathematics, and that locally convex spaces, together with appropriate ad hoc topological constructions, might su¢ ce for most constructive analysis. Work begun by us ve years ago suggests that, on the contrary, there is at least one constructive approa...
متن کاملPrecompact Apartness Spaces
We present a notion of precompactness, and study some of its properties, in the context of apartness spaces whose apartness structure is not necessarily induced by any uniform one. The presentation lies entirely with a Bishop-style constructive framework, and is a contribution to the ongoing development of the constructive theories of apartness and uniformity.
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ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 119 شماره
صفحات -
تاریخ انتشار 2003