On fuzzy semi-preopen sets and fuzzy semi-precontinuity

Some Weaker Forms of Fuzzy Faintly Open Mappings

“…• Fuzzy semi preopen (Fuzzy semi preclosed) set [6] if there exists a fuzzy preopen (fuzzy preclosed) set m (n ) such that m ≤ λ ≤ cl m (Int n ≤ λ ≤ n).…”

“…We find a large community of mathematicians who has already contributed to a large extent in this direction. For example, Chang [3] has introduced fuzzy openness (fuzzy closedness), Azad [1] introduced fuzzy semi openness (fuzzy semi closedness), Bin Shahna [2] introduced fuzzy pre openness (fuzzy pre closedness) and fuzzy α -openness (fuzzy α -closedness), Thakur and Singh [6] introduced fuzzy semi pre openness (fuzzy semi pre closedness) and Hakeem A. Othman [4] has introduced fuzzy sp-openness (fuzzy sp-closedness) and they establish their various characteristic properties. In this paper, I introduce and study ten weak forms of faintly open mappings, called fuzzy faintly semi open (fuzzy faintly semi closed), fuzzy faintly preopen (fuzzy faintly preclosed), fuzzy faintly α-open (fuzzy faintly α-closed), fuzzy faintly semi preopen (fuzzy faintly semi preclosed) and fuzzy faintly sp-open (fuzzy faintly sp-closed) mappings, I study their basic properties and their relationship with other types of fuzzy open (closed) mappings.…”

A New Notion of Sp-Compact L-Fuzzy Sets

“…Each member of δ is called an open L-set and its quasi-complement is called a closed L-set. The semipreopen set and semi-preclosed set are defined in [0,1]-topological space in [11]. Analogously we can generalize it to L-subset in L-topological spaces.…”

“…Since every semi-open L-set is semi-preopen [2,11], every SP-compact L-set is semi-compact. Example 3.3 shows that semi-compact L-set needn't be SP-compact.…”

“…Thakur and Singh extended these concepts to [0,1]-topological spaces [11] in the Chang's [4] sense. In [2], we introduced the concept of SP-compactness in L-topological spaces.…”