Two new L-fuzzy topologies on R ( L)

Abstract

In this paper, two new topologies, τ′ 1, τ′ 2 on R ( L) are constructed. Using τ′ i , we produced two L-fuzzy topologies η′ i on R( L) other than the L-fuzzy topology T introduced by Hutton. We have proved that η′ 1 is finer than η′ 2 and η′ 2 is finer than T. η′ 2 is the coarsest among the induced L-fuzzy topologies which are finer than T. We have shown that ( L R( L) , η i ), the induced space of ( R ( L), τ′ i , possesses many good properties, such as stronger separation, suitability, etc. We proved that closed interval ([ a, b] ( L), ν 2|[ a, b] ( L)) is closed, connected and N-compact. The addition and multiplication defined on R ( L) by Rodabaugh, are still jointly continuous.