CONVERGENCE APPROACH SPACES AND APPROACH SPACES AS LATTICE-VALUED CONVERGENCE SPACES

We show that the category of convergence approach spaces is a simultaneously re ective and core ective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously re ective and core ective subcategory of the category of lattice-valued pretopological spaces and that the category of approach spaces is a core ective subcategory of a category of lattice-valued topological convergence spaces.