منابع مشابه
Similarity, topology, and uniformity
We generalize various notions of generalized metrics even further to one general concept comprising them all. For convenience, we turn around the ordering in the target domain of the generalized metrics so that we speak of similarity instead of distance. Starting from an extremely general situation without axioms, we examine which axioms or additional properties are needed to obtain useful resu...
متن کاملSimilarity, Topology, and Uniformity Dedicated to Dieter Spreen on the occasion of his 60th birthday
We generalize various notions of generalized metrics even further to one general concept comprising them all. For convenience, we turn around the ordering in the target domain of the generalized metrics so that we speak of similarity instead of distance. Starting from an extremely general situation without axioms, we examine which axioms or additional properties are needed to obtain useful resu...
متن کاملApartness, Topology, and Uniformity: a Constructive View
The theory of apartness spaces, and their relation to topological spaces (in the point—set case) and uniform spaces (in the set—set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by even a uniform structure.
متن کاملA topology induced by uniformity on BL-algebras
BL-algebras have been invented by P. Hájek [3] in order to provide an algebraic proof of the completeness theorem of “Basic Logic” (BL, for short) arising from the continuous triangular norms, familiar in the fuzzy logic framework. The above notion is generalized to an algebraic system in which the required conditions are fulfilled (Definition 2.1). Filters in BL-algebras are also defined. A fi...
متن کاملOne Setting for All: Metric, Topology, Uniformity, Approach Structure
For a complete lattice V which, as a category, is monoidal closed, and for a suitable Setmonad T we consider (T,V)-algebras and introduce (T,V)-proalgebras, in generalization of Lawvere’s presentation of metric spaces and Barr’s presentation of topological spaces. In this lax-algebraic setting, uniform spaces appear as proalgebras. Since the corresponding categories behave functorially both in ...
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ژورنال
عنوان ژورنال: The Journal of Logic and Algebraic Programming
سال: 2010
ISSN: 1567-8326
DOI: 10.1016/j.jlap.2009.02.003