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

Authors

  • Jinming Fang Department of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R. China
  • Qian Yu 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.

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Journal title

volume 14  issue 3

pages  121- 138

publication date 2017-06-29

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