A new approach to -, -Urysohn, and -completely Hausdorff axioms

Some separation axioms in L-topological spaces

“…Therefore for ∀P ∈ η − (x λ ), ∀Q ∈ η − (y λ ), we have P ∨ Q ≤ 0.7 * . Hence (L X , δ) is not a sub-T 2 space.2 Now, we discuss the relation between the sub-separation axioms and other separation axioms presented by Shi [14], Wang [16], Gu and Zhao [4]. The following two examples show that sub-T 2 need not imply L-T 2 and L-T 2 also need not imply sub-T 2 .…”

“…In this section, we make a comparison between separation axioms defined in this paper and those presented by Chen and Meng [2], Fang and Ren [3], Gu and Zhao [4], Ganguly and Saha [5], Kubiak [7], Kandil and El-Shafee [8], Shi [14],Shi and Chen [15] and Wang [16], and offer a lot of examples to show the relations between them. At first, we show that the sub-separation axioms defined in this paper are harmonious.…”

“…Separation is an essential part of fuzzy topology, on which a lot of work have been done [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In 1983, Liu [9] introduced the sub-T 0 axiom, for underlying lattice L being a completely distributive DeMorgan algebra, in terms of closed sets and proved that the fuzzy real line and the fuzzy unit interval satisfy this axiom.…”

Fuzzifying pseudo-quasi-metric topologies on the fuzzy real line

“…To reflect the characteristics of pointwise L-topology, i.e., the relation between a fuzzy point and its Q-neighborhoods (or R-neighborhoods) [9], a theory of pointwise uniformities and a theory of pointwise metrics were introduced on completely distributive lattices and in L-fuzzy set theory(see [11,12]). Many ideal results in general topology were generalized to L-topology [14,15]. It was proved that the L-fuzzy real line is pointwise pseudo-metrizable and the pointwise pseudo-metric function on the L-fuzzy real line was given [13].…”