2 NEW L-FUZZY TOPOLOGIES ON R(L)

In this paper, two new topologies tau(1)', tau(2)' on R(L) are constru cted. Using tau(i)', we produced two L-fuzzy topologies eta(i)' on R(L ) other than the L-fuzzy topology T introduced by Hutton. We have prov ed that eta(1)' is finer than eta(2)' and eta(2)' is finer than T. eta (2)' is the coarsest among the induced L-fuzzy topologies which are fi ner than T. We have shown that (L(R(L)), eta(i)), the induced space of (R(L), eta(i)), possesses many good properties, such as stronger separ ation, suitability, etc. We proved that closed interval ([a, b](L), et a(2)\[a, b](L)) is closed, connected and N-compact. The addition and m ultiplication defined on R(L) by Rodabaugh, are still jointly continuo us.