Article ID Journal Published Year Pages File Type
390419 Fuzzy Sets and Systems 2012 20 Pages PDF
Abstract

We define a category of stratified L-generalized convergence spaces for the case where the lattice is an enriched cl-premonoid. We then investigate some of its categorical properties and those of its subcategories, in particular the stratified L-principal convergence spaces and the stratified L-topological convergence spaces. For some results we need to introduce a new condition on the lattice (which is always true in the case where the lattice is a frame, but not always true in the more general case). As examples where we may apply the more general lattice context we examine the stratified L-topological spaces and probabilistic limit spaces. We show that the category of stratified L-topological spaces is a reflective subcategory of our category and that the category of probabilistic limit spaces under a T-norm is both a reflective and a coreflective subcategory of our category if we choose the lattice context appropriately.

► We extend lattice-valued convergence spaces to enriched cl-premonoid L. ► We study the categorical properties of our category and of some of its subcategories. ► The category of stratified L-topological spaces is a reflective subcategory of our category. ► The category of probabilistic limit spaces under a T-norm is both a reflective and a coreflective subcategory of our category.

Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence
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