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

Document Type : Research Paper

Author

Department of Statistics, Rhodes University, 6140 Grahamstown, South Africa

Abstract

We show that the category of convergence approach spaces is a
simultaneously reective and coreective 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 reective and coreective subcategory of
the category of lattice-valued pretopological spaces and that the category of
approach spaces is a coreective subcategory of a category of lattice-valued
topological convergence spaces

Keywords


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