Employing the notions of the strong $L$-topology introduced by Zhangand the $L$-frame introduced by Yao  and the concept of $L$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf St$L$-Top} of strong$L$-topological spaces, {bf S$L$-Loc} of strict $L$-locales and{bf $L$-EnTopSys} of $L$-enriched topological systems. All of theseconcepts are ...

For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions and on the space M (Ω) of bounded Borel measures. The important fact here is that the dual of Cb(Ω) with the strict topology is M (Ω). We pursue the approach via bi-continuous semigroups, but we also show that the class of bi-continuous semigroups on Cb(Ω) with respect to the compact-open to...

The strict topology j3 on the space C(S) of bounded complex valued continuous functions on a locally compact space 5 was introduced by R. C. Buck [ l ] and has been studied by Glicksberg [4] and Wells [9], Among the problems in mathematics which have seen successful applications of the strict topology are various ones in spectral synthesis (Herz [6]) and spaces of bounded analytic functions (Sh...

1. Let X be a locally compact Hausdorff space, C(X)ß the locally convex topological vector space obtained from all bounded complex continuous functions on X by employing the strict topology [2]. The present note is devoted to a version of Bishop's generalized StoneWeierstrass theorem [l] applicable to certain subspaces of C(X)ß-, essentially it is a footnote to an earlier paper [4], in which a ...