Using an algebraic property, the completely distributive law, we have ever given out a characterization of the semicontinuity of lattice-valued mappings. How about the inverse implication? That is to say, can we analy...Using an algebraic property, the completely distributive law, we have ever given out a characterization of the semicontinuity of lattice-valued mappings. How about the inverse implication? That is to say, can we analytically characterize the completely distributive law? Moreover, can we characterize the completely distributive law in terms of fuzzy topology? The purpose of this note is to answer affirmatively these questions for the infinitely distributive lattices. This study connecting algebra with analysis and topology seems to be rather interesting.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘Using an algebraic property, the completely distributive law, we have ever given out a characterization of the semicontinuity of lattice-valued mappings. How about the inverse implication? That is to say, can we analytically characterize the completely distributive law? Moreover, can we characterize the completely distributive law in terms of fuzzy topology? The purpose of this note is to answer affirmatively these questions for the infinitely distributive lattices. This study connecting algebra with analysis and topology seems to be rather interesting.
