Abstract
In this paper, several types of enriched (L,M)-fuzzy convergence spaces are introduced, including enriched (L,M)-fuzzy Kent convergence spaces, enriched (L,M)-fuzzy limit spaces, pretopological enriched (L,M)-fuzzy convergence spaces, topological enriched (L,M)-fuzzy convergence spaces and enriched (L,M)-fuzzy Choquet convergence spaces. These concepts generalize the concepts of Kent convergence spaces, of limit spaces, of pretopological convergence spaces, of topological convergence spaces and of Choquet convergence spaces in general topology to the setting of (L,M)-fuzzy topology. Also, their categorical properties and their mutual categorical relations are investigated.
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