Ideal-valued topological structures


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. © 2010 Elsevier B.V. All rights reserved.

DOI: 10.1016/j.fss.2010.03.007

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@article{Garca2010IdealvaluedTS, title={Ideal-valued topological structures}, author={Javier Guti{\'e}rrez Garc{\'i}a and Tomasz Kubiak and Alexander P. Sostak}, journal={Fuzzy Sets and Systems}, year={2010}, volume={161}, pages={2380-2388} }