Upper semicontinuous fuzzy sets and applications

L-pre-separation axioms in (2, L)-topologies based on complete residuated lattice-valued logic

“…Definition 2.10 (Höhle [4], Höhle andŠostak [6], Kubiak [9],Šostak [13], [17]). An (M, L)-fuzzy topology (we pre-…”

“…In [4,5,9,13,17] the concept of (M, L)-fuzzy topology was appeared as a function τ : M X −→ L where X is an ordinary set; and M and L are some types of lattices. We prefer to use the symbol (M, L)-topology instead of (M, L)-fuzzy topology.…”

“…The concept of (2, L)-topology (L-fuzzifying topology) appeared in [4] by Höhle under the name "L-fuzzy topology" (cf. Definition 4.6, Proposition 4.11 in [4]).…”

“…Definition 4.6, Proposition 4.11 in [4]). In the case of L = I where I is the closed unit interval [0, 1] the terminology "L-fuzzifying topology" traces back to Ying (cf.…”

“…In Section 3, we introduce and study ( 4 -, L-pre-R 0 -, L-pre-R 1 -separation axioms in (2, L)-topologies and study the relation of it with L-separation axioms. In Section 6, relations among these separation axioms are considered.…”