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

Document Type: Research Paper

Authors

Department of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R. China

Abstract

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


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