A note on compactness in ${\bf L}$-fuzzy pretopological spaces

Mashhour, A. S.; Ramadan, A.A.; El-Monsef, M. E. Abd

doi:10.1216/rmjm/1181073172

“…The concepts of a fuzzy pretopology, 1 compactness and 2  compactness were introduced and studied by Badard in [2]. Mashour et al in [8] introduced and studied the concepts of countable compactness and lindelöf in L  fuzzy pretoological spaces. Khedr et al in [6] introduced the definition of a fuzzy soft pretopology.…”

Section: Introductionmentioning

confidence: 99%

Soft Compactness of Fuzzy Soft Pretopological Spaces

2020

Assiut University Journal of Multidisciplinary Scientific Resea

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“…This paper consists of three sections, section one is called "Introduction", where the contents of this paper are explained and fundamental concepts are given. The concept of a preopen set lies in (1), where they have introduced "a preopen set when  and its properties such as the intersection of an open set and a preopen set is preopen".…”

Section: Introductionmentioning

confidence: 99%

“…preclosed)" you see it in (1). References (1) and (3) show that, "the intersection of all preclosed sets containing A is called the preclosure of , denoted by , which is the smallest preclosed set containing ". But (4) and (5) introduce a preneighborhood and a preopen function respectively.…”

Section: Introductionmentioning

confidence: 99%

Results on a Pre-T_2 Space and Pre-Stability

Jasim¹

2019

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This paper contains an equivalent statements of a pre- space, where are considered subsets of with the product topology. An equivalence relation between the preclosed set and a pre- space, and a relation between a pre- space and the preclosed set with some conditions on a function are found. In addition, we have proved that the graph of is preclosed in if is a pre- space, where the equivalence relation on is open. On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that a pre-stable ( pre-stable) set is positively invariant (invariant), and we add a condition on this set to prove the converse. Finally, a relationship between, (i) a pre-stable ( pre-stable) set and its component (ii) a pre- space and a (positively critical point) critical point, are gotten.

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“…This paper consists of three sections, section one is called "Introduction", where the contents of this paper are explained and fundamental concepts are given. The concept of a preopen set lies in (1), where they have introduced "a preopen set 𝐴 when 𝐴  𝐴 𝑜 and its properties such as the intersection of an open set and a preopen set is preopen". Also, "the union of any family of preopen sets is a preopen set", you can find it in (2).…”

Section: Introductionmentioning

confidence: 99%

“…While "its complement (i.e. preclosed)" you see it in (1). References (1) and (3) show that, "the intersection of all preclosed sets containing A is called the preclosure of 𝐴, denoted by 𝐴 𝑝 , which is the smallest preclosed set containing 𝐴".…”

Section: Introductionmentioning

confidence: 99%

Results on a Pre-T_2 Space and Pre-Stability

Jasim¹

2019

View full text Add to dashboard Cite

This paper contains an equivalent statements of a pre- space, where are considered subsets of with the product topology. An equivalence relation between the preclosed set and a pre- space, and a relation between a pre- space and the preclosed set with some conditions on a function are found. In addition, we have proved that the graph of is preclosed in if is a pre- space, where the equivalence relation on is open. On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that a pre-stable ( pre-stable) set is positively invariant (invariant), and we add a condition on this set to prove the converse. Finally, a relationship between, (i) a pre-stable ( pre-stable) set and its component (ii) a pre- space and a (positively critical point) critical point, are gotten.

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A note on compactness in ${\bf L}$-fuzzy pretopological spaces

Cited by 6 publications

References 10 publications

Soft Compactness of Fuzzy Soft Pretopological Spaces

Soft Compactness of Fuzzy Soft Pretopological Spaces

Results on a Pre-T_2 Space and Pre-Stability

Results on a Pre-T_2 Space and Pre-Stability

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