Results on soft extremally disconnectedness of soft topological spaces

Asaad, Baravan A.

doi:10.22436/jmcs.017.04.02

Cited by 30 publications

(10 citation statements)

References 2 publications

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“…4. soft hyperconnected [30] if every nun-null soft open set is soft dense. 5. soft extremally disconnected [22] if Cl τ (ξ, A) is soft open for every (ξ, A) ∈ τ. Theorem 1. [15,20] A soft closed set in a soft compact (resp.…”

Section: Definition 15mentioning

confidence: 99%

“…The authors in [20] have discussed the concepts of soft connectedness and soft paracompactness. The authors in [21] have introduced a concept of soft hyperconnected spaces, and the authors [22] have studied a concept of soft extremally disconnected spaces. Kharal and Ahmad [23] were the first one who introduced the concept of soft mappings and proved main properties.…”

Section: Introductionmentioning

confidence: 99%

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Sum of Soft Topological Spaces

2020

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In this paper, we introduce the concept of sum of soft topological spaces using pairwise disjoint soft topological spaces and study its basic properties. Then, we define additive and finitely additive properties which are considered a link between soft topological spaces and their sum. In this regard, we show that the properties of being p-soft T i , soft paracompactness, soft extremally disconnectedness, and soft continuity are additive. We provide some examples to elucidate that soft compactness and soft separability are finitely additive; however, soft hyperconnected, soft indiscrete, and door soft spaces are not finitely additive. In addition, we prove that soft interior, soft closure, soft limit, and soft boundary points are interchangeable between soft topological spaces and their sum. This helps to obtain some results related to some important generalized soft open sets. Finally, we observe under which conditions a soft topological space represents the sum of some soft topological spaces.

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Section: Definition 15mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sum of Soft Topological Spaces

2020

Self Cite

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“…(ii) soft extremally disconnected [37] if the closure of every soft open set is soft open. To study the properties that preserved under soft b -homeomorphism maps, the concept of a soft b-irresolute map will be presented in this work under the name of a soft b -continuous map.…”

Section: Definition 210 ([4])mentioning

confidence: 99%

Weak Forms of Soft Separation Axioms and Fixed Soft Points

Al-shami

Abo-Tabl

Asaad

2020

Fuzzy Information and Engineering

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Realizing the importance of separation axioms in classifications of topological spaces and studying certain properties of fixed points, we formulate new soft separation axioms, namely tt-soft bT i (i = 0, 1, 2, 3, 4) and tt-soft b-regular spaces. Their definitions depend on three factors: soft b-open sets, total belong and total non-belong relations. In fact, they are genuine generalizations of p-soft T i -spaces in the cases of i = 0, 1, 2. With the help of examples, we study the relationships between them as well as with soft bT i (i = 0, 1, 2, 3, 4) and soft b-regular spaces. Some interesting properties of them are obtained under the conditions of soft hyperconnected and extended soft topological spaces. Also, we show that they are preserved under finite product soft spaces and soft b -homeomorphism mappings. Finally, we introduce a concept of b-fixed soft points and investigate its main properties.

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“…e work of Shabir and Nazs [7], in particular, was crucial in establishing the field of soft topology. After that various classes of soft topological spaces have been proposed, such as: soft compact [8], soft connected [9], soft paracompact [9], soft extremely disconnected [10], and soft separable spaces [11], soft J-spaces [12], soft Menger spaces [13] and soft separation axioms [11,14]. At this point, it is worth remarking that not all classical results in topology are true in soft topology, see eorem 4 in [15].…”

Section: Introductionmentioning

confidence: 99%

Maximal Soft Compact and Maximal Soft Connected Topologies

Ghour

Ameen

2022

Applied Computational Intelligence and Soft Computing

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In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal, and some are minimal with respect to specific soft topological properties. We study the properties of soft compact and soft connected topologies that are maximal. Particularly, we prove that a maximal soft compact topology has identical families of soft compact and soft closed sets. We further show that a maximal soft compact topology is soft T 1 , while a maximal soft connected topology is soft T 0 . Lastly, we establish that each soft connected relative topology to a maximal soft connected topology is maximal.

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Results on soft extremally disconnectedness of soft topological spaces

Cited by 30 publications

References 2 publications

Sum of Soft Topological Spaces

Sum of Soft Topological Spaces

Weak Forms of Soft Separation Axioms and Fixed Soft Points

Maximal Soft Compact and Maximal Soft Connected Topologies

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