Compactness in MV-Topologies: Tychonoff Theorem and Stone-Cech Compactification

Luz Victoria De La Pava; Ciro Russo

doi:10.1007/s00153-019-00679-6

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arXiv · 1608.02923

Compactness in MV-Topologies: Tychonoff Theorem and Stone-Cech Compactification

Luz Victoria De La Pava·Ciro Russo

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Abstract

In this paper, we discuss some questions about compactness in MV-topological spaces. More precisely, we first present a Tychonoff theorem for such a class of fuzzy topological spaces and some consequence of this result, among which, for example, the existence of products in the category of Stone MV-spaces and, consequently, of coproducts in the one of limit cut complete MV-algebras. Then we show that our Tychonoff theorem is equivalent, in ZF, to the Axiom of Choice, classical Tychonoff theorem, and Lowen's analogous result for lattice-valued fuzzy topology. Last, we show an extension of the Stone-Cech compactification functor to the category of MV-topological spaces, and we discuss its relationship with previous works on compactification for fuzzy topological spaces.

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Luz Victoria De La Pava, Ciro Russo. 2016-08-09. Compactness in MV-Topologies: Tychonoff Theorem and Stone-Cech Compactification. https://doi.org/10.1007/s00153-019-00679-6

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