A First—order Constructive Theory of Nearness Spaces
نویسنده
چکیده
A first—order axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for constructive topology.
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 کاملApartness spaces as a framework for constructive topology
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.
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 کاملA constructive theory of point-set nearness
An axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for topology.
متن کاملNear semigroups on nearness approximation spaces
In this paper, our approach is to study properties of approximations on nearness approximation spaces. Afterwards, our aim is to define near semigroups and near ideals on near approximation spaces. We introduce some properties of these near structures. The nearness of sets and, in particular, the nearness of algebraic structures on nearness approximation spaces fits within the milieu of fuzzy s...
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تاریخ انتشار 2000