Abstract

We study a category of lattice-valued metric spaces that contains many categories of lattice-valued metric spaces studied before. Furthermore, introducing suitable convergence structures, we are able to show that the category of these lattice-valued metric spaces is a coreflective subcategory of the category of lattice-valued convergence spaces and we even characterize lattice-valued metric spaces by convergence.

Keywords: $LM$-fuzzy metric space; $L$-convergence tower space; $M$-valued distance distribution function.

MSC: 54A20, 54A40, 54E35, 54E70

Pages:  31--44     

Volume  71 ,  Issue  1-2 ,  2019