Topologies on M-Valued Sets

Ulrich Höhle
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Ulrich Höhle: Bergische Universität, Fachbereich Mathematik

Chapter Chapter 10 in Many Valued Topology and its Applications, 2001, pp 331-360 from Springer

Abstract: Abstract The purpose of this chapter is to show that the categorical foundations of topology (cf. Part I) can be applied to a monadic setting in which the base category is not given by SET, In the following considerations we will use the category of separated M-valued sets as base category. Anticipating the terminology introduced in [53] we will show that topologies on separated M-valued sets can be viewed as sheaves of B-valued topologies over the underlying monoid M (cf. Subsection 10.2.1). As a by-product of these developments we obtain a solution of the topological subspace problem for many valued topological spaces — i.e. the problem to find a construction which permits to associate a topological subspace structure in the sense of Definition 3.1.7 with a lattice valued map.

Keywords: Heyting Algebra; Topological Subspace; Power Object; Interior Operator; Categorical Foundation (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-1-4615-1617-0_11

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