THE CATEGORY OF T-CONVERGENCE SPACES AND ITS CARTESIAN-CLOSEDNESS

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of \top-filters, namely \top-convergence spaces, and show the category of \top-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete MV-algebra, a close relation between the category of\top-convergence spaces and that of strong L-topological spaces is established. In details, we show that the category of strong L-topological spaces is concretely isomorphic to that of strong L-topological \top-convergence spaces categorically and bireflectively embedded in that of \top-convergence spaces.

Keywords:

T-lter , T-convergence , Cartesian-closedness , Topological category , Reflection , Strong L-topology