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Topologies on M-Valued Sets

In: Many Valued Topology and its Applications

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  • Ulrich Höhle

    (Bergische Universität, Fachbereich Mathematik)

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.

Suggested Citation

  • Ulrich Höhle, 2001. "Topologies on M-Valued Sets," Springer Books, in: Many Valued Topology and its Applications, chapter 0, pages 331-360, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-1617-0_11
    DOI: 10.1007/978-1-4615-1617-0_11
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