On initial and final fuzzy uniform structures

On initial and final L-topological groups

“…is an L-topology on X for which conditions (1) and (2) of the initial lift in L-Top are fulfilled [12,3]. That is, = i∈I f ← i i is the initial L-topology of ( i ) i∈I with respect to (f i ) i∈I , and f ← i i is the initial L-topology of i with respect to f i .…”

“…It is shown in [14,3] that the infimum of the family (f → i ( i )) i∈I with respect to the finer relation on…”

The relation between GTi-spaces and fuzzy proximity spaces, G-compact spaces, fuzzy uniform spaces

“…for all x 2 X [4,10]. A fuzzy uniform structure U on X is called separated if for all x; y 2 X with x 6 ¼ y there is u 2 L X ÂX such that UðuÞ ¼ 1 and uðx; yÞ ¼ 0.…”

Images and preimages of -filterbases

“…Höhle et al [14,15] introduced the notion of L-filter on a complete quasi-monoidal lattice (including GL-monoid [10,11]) L instead of a completely distributive lattice [2][3][4]7,8] or the unit interval [3,4] as an extension of fuzzy filters [12,13,17]. The notion of L-filter facilitated to study L-fuzzy topologies [15,18] and L-fuzzy uniform spaces [2,22].…”

“…The notion of L-filter facilitated to study L-fuzzy topologies [15,18] and L-fuzzy uniform spaces [2,22]. Let L be a complete lattice and : X → Y a function.…”