Fuzzy quasi-proximities and fuzzy quasi-uniformities
Fuzzy Sets and Systems
Fuzzy uniformities induced by fuzzy proximities
Fuzzy Sets and Systems
Uniformity and proximity of L-fuzzy topological spaces
Fuzzy Sets and Systems - Mathematics and Fuzziness, Part II
Theory of topological molecular lattices
Fuzzy Sets and Systems
Gradations of uniformity and gradations of proximity
Fuzzy Sets and Systems
Pointwise uniformities in fuzzy set theory
Fuzzy Sets and Systems
Fuzzy proximity ordered spaces
Fuzzy Sets and Systems
On S-quasi-fuzzy proximity spaces
Fuzzy Sets and Systems
Pointwise pseudo-metrics in L-fuzzy set theory
Fuzzy Sets and Systems
L-proximities and totally bounded pointwise L-uniformities
Fuzzy Sets and Systems - Topology
Fuzzy Sets and Systems
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First it is proved that the category of pointwise quasi-uniform spaces and pointwise quasi-uniformly continuous morphisms is topological. Then the concept of pointwise S-quasi-proximity on lattice-valued fuzzy set theory is introduced in such a way as to be compatible with pointwise quasi-uniformity and pointwise p.q. metric. Each co-topology can be induced by a pointwise S-quasi-proximity. When a valued lattice is a completely distributive lattices equipped with an order-reversing involution, the concept of pointwise S-proximity can be defined by means of pointwise S-quasi-proximity. The relation between pointwise S-(quasi-)proximities and pointwise (quasi-)uniformities is discussed. It is proved that the category of pointwise S-quasi-proximity spaces is isomorphic to the category of totally bounded pointwise quasi-uniform spaces. The category of pointwise S-proximity spaces is isomorphic to a subcategory of totally bounded pointwise uniform spaces. Hence they are topological.