Fuzzy topological spaces with conical neighborhood systems

In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer’s diagonal condition, the other approach extends the Gähler’s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p-topologicalness in stratified L-generalized convergence spaces are established. Furthermore, the lower and upper p-topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p-topological modification behaves reasonably well relative to final (resp., initial) structures.

Section: Remarkmentioning

confidence: 77%

Section: -Filters and Stratified L-filtersmentioning

confidence: 99%

See 1 more Smart Citation

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

Li¹

2019

“…The subsethood degree of µ, ν, denoted as S X (µ, ν), is defined by [44][45][46] Lemma 1. [31,42,47] Let f : X −→ Y be a function and…”

Section: Preliminariesmentioning

confidence: 99%

p-Regularity and p-Regular Modification in ⊤-Convergence Spaces

Jin

Lang

2019

Fuzzy convergence spaces are extensions of convergence spaces. ⊤-convergence spaces are important fuzzy convergence spaces. In this paper, p-regularity (a relative regularity) in ⊤-convergence spaces is discussed by two equivalent approaches. In addition, lower and upper p-regular modifications in ⊤-convergence spaces are further investigated and studied. Particularly, it is shown that lower (resp., upper) p-regular modification and final (resp., initial) structures have good compatibility.

“…In [25], Lai and Zhang introduced a kind of L-topological space, called conical neighborhood space (CNS). We do not give the definition of CNS here; please see Definition 5.1 in [25]. Lai and Zhang proved that the mentioned L-topological spaces have the following inclusive relation:…”

Section: Definition 3 ([14])mentioning

confidence: 99%

Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces

Jin

Jiang

2019

Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ⊤-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending Gähler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ⊤-convergence space with their Fischer diagonal condition just characterizes strong L-topology—a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ⊤-convergence space with our Fischer diagonal condition precisely characterizes topological generated L-topology—a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on Gähler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence).