Ideals on fuzzy topological spaces

Separation axioms on fuzzy ideal topological spaces in 𝑺 ̆ ostak‘s sense

“…Definition 1.2: A mapping ℐ: → is called a fuzzy ideal on X if it satisfies the following conditions (Saber and Abdel-Sattar, 2014):…”

“…such that if ℬ ∈ ( . ) and ℐ( ) ≥ then there is at least one ∈ for which ℬ( ) + ( ) − 1 > ( ) (Saber and Abdel-Sattar, 2014).…”

“…After that several authors (Chattopadhyay et al, 1992;Chattopadhyay and Samanta, 1993;El Gayyar et al, 1994;Kim and Ko, 2001;Ramadan, 1992;Ramadan et al, 2001) have introduced the smooth definition and studied smooth fuzzy topological spaces being unaware of Sostak (1985) works. In fuzzy topology, by introducing the notion of ideal, (Sarkar, 1997), and several other authors (Hatir and Jafari, 2007;Nasef and Mahmoud, 2002;Saber and Abdel-Sattar, 2014;Zahran et al, 2009;Alsharari and Saber, 2019;Saber and Alsharari, 2018) carried out such analysis. Throughout this paper, let X be a nonempty set, = [0.1], 0 = (0.1] and denote the set of all fuzzy subsets of .…”

Ideals on Generalized Topological Spaces

“…They proved some basic properties for the local closure function, and also introduced two new topologies obtained from the original one using the local closure function. Afterwards, many properties in topological spaces have been explored by various researchers ( [20], [21], [22], [23], [24], [25])…”

Compactness in L-smooth ideal topological spaces

“…Many authors [8,9,11,14,16,17,18,20,24,27] studied the structures of fuzzy topology and the structures of fuzzy compactness, fuzzy ideals and fuzzy smooth ideals. Ramadan, Abdel-Sattar and Kim [19] studied the concept of a smooth ideals in [0,1]-smooth topological spaces.…”