Ideal-valued topological structures

Javier Gutiérrez García

doi:10.1016/j.fss.2010.03.007

Ideal-valued topological structures

2010-09-01

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Javier Gutiérrez García

DOI：10.1016/j.fss.2010.03.007

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Abstract

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With L a complete lattice and M a continuous lattice, this paper demonstrates an adjunction between M-valued L-topological spaces (i.e. (L,M)-topological spaces) and Idl(M)-valued L-topological spaces where Idl(M) is the complete lattice of all ideals of M. It is shown that the right adjoint functor provides a procedure of generating (L,M)-topologies from antitone families of (L,M)-topologies. This procedure is then applied to give an internal characterization of joins in the complete lattice of all (L,M)-topologies on a given set. (c) 2010 Elsevier B.V. All rights reserved.

Keywords:

Fuzzy topology

Continuous lattice

Ideal

Adjoint functors

Principal ideal functor

Sup functor

(L,M)-topological space

Ideal-valued topological structures

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