Elsevier

Fuzzy Sets and Systems

Volume 101, Issue 3, 1 February 1999, Pages 469-475
Fuzzy Sets and Systems

On two weaker forms of continuous order-homomorphisms

https://doi.org/10.1016/S0165-0114(97)00103-6Get rights and content

Abstract

The aim of this paper is to find further connections between two different current researches on fuzzy topology: the one based on the concepts of neighborhood, filter and Zadeh function, and the other based on the concepts of remote neighborhood, ideal and order-homomorphism on fuzzy lattices. To approach this, the paper studies two weaker forms of continuous order-homomorphisms, the semi-continuous order-homomorphism and the weakly semi-continuous order-homomorphism between L-fuzzy topological spaces. These order-homomorphisms can be characterized in each of the notions: remote-neighborhood, neighborhood, ideal, filter and molecular net. In addition, some relations connecting weakly semi-continuous order-homomorphisms, semi-Hausdorff L-fts and Urysohn L-fts have also been established.

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This work was supported by the Fund for Excellent Young University Teachers of the State Educational Commission of China (Grant No. 1994357).

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