we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

in this paper the concept of metacompactness in l-topologicalspaces is introduced by means of point finite families of l-fuzzy sets. thisfuzzy metacompactness is a natural generalization of lowen fuzzy compactness.further a characterization of fuzzy metacompactness in the weakly inducedl-topological spaces is also obtained.

This paper presents characterizations of M-fuzzifying matroids bymeans of two kinds of fuzzy operators, called M-fuzzifying derived operatorsand M-fuzzifying difference derived operators.

In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for thebasis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroidis equivalent to a mapping which satisfies the basis ...

in this paper, a pointwise pseudo-metric function on the l-realline is constructed. it is proved that the topology induced by this pointwisepseudo-metric is the usual topology.

In this paper, a pointwise pseudo-metric function on the L-realline is constructed. It is proved that the topology induced by this pointwisepseudo-metric is the usual topology.