Displaying similar documents to “Some methods for generating topologies by relations.”

Topological Interpretation of Rough Sets

Adam Grabowski (2014)

Formalized Mathematics

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Rough sets, developed by Pawlak, are an important model of incomplete or partially known information. In this article, which is essentially a continuation of [11], we characterize rough sets in terms of topological closure and interior, as the approximations have the properties of the Kuratowski operators. We decided to merge topological spaces with tolerance approximation spaces. As a testbed for our developed approach, we restated the results of Isomichi [13] (formalized in Mizar in...

Further characterizations of boundedly UC spaces

Ľubica Holá, Dušan Holý (1993)

Commentationes Mathematicae Universitatis Carolinae

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Following the paper [BDC1], further relations between the classical topologies on function spaces and new ones induced by hyperspace topologies on graphs of functions are introduced and further characterizations of boundedly UC spaces are given.

Relational Formal Characterization of Rough Sets

Adam Grabowski (2013)

Formalized Mathematics

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The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based...

P-adic Spaces of Continuous Functions I

Athanasios Katsaras (2008)

Annales mathématiques Blaise Pascal

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Properties of the so called θ o -complete topological spaces are investigated. Also, necessary and sufficient conditions are given so that the space C ( X , E ) of all continuous functions, from a zero-dimensional topological space X to a non-Archimedean locally convex space E , equipped with the topology of uniform convergence on the compact subsets of X to be polarly barrelled or polarly quasi-barrelled.