More notions and mappings via somewhere dense sets

Al-shami, Tareq M.; Noiri, Takashi

doi:10.1007/s13370-019-00700-4

Cited by 19 publications

(9 citation statements)

References 10 publications

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“…In the upcoming work, we plan to explore functionally regular and functionally normal spaces. Also, we generalize the presented concepts presented in this manuscript using somewhere dense sets and SD-continuous maps given in [7,16,17].…”

Section: Proofmentioning

confidence: 99%

Functionally Separation Axioms on General Topology

Mhemdi

Al-shami

2021

Journal of Mathematics

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In this paper, we define a new family of separation axioms in the classical topology called functionally T i spaces for i = 0,1,2 . With the assistant of illustrative examples, we reveal the relationships between them as well as their relationship with T i spaces for i = 0,1,2 . We demonstrate that functionally T i spaces are preserved under product spaces, and they are topological and hereditary properties. Moreover, we show that the class of each one of them represents a transitive relation and obtain some interesting results under some conditions such as discrete and Sierpinski spaces.

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Section: Proofmentioning

confidence: 99%

Functionally Separation Axioms on General Topology

Mhemdi

Al-shami

2021

Journal of Mathematics

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“…Many studies have appeared recently and dealt with generalizations of topological near-open sets [1,2] and the possibility of using them in many life applications, including their use in data reduction and reaching some new decisions and conclusions. Rough set theory is a modern approach for reasoning about data [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Topological Approaches for Rough Continuous Functions with Applications

et al. 2021

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In this paper, we purposed further study on rough functions and introduced some concepts based on it. We introduced and investigated the concepts of topological lower and upper approximations of near-open sets and studied their basic properties. We defined and studied new topological neighborhood approach of rough functions. We generalized rough functions to topological rough continuous functions by different topological structures. In addition, topological approximations of a function as a relation were defined and studied. Finally, we applied our approach of rough functions in finding the images of patient classification data using rough continuous functions.

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“…These two definitions of the inverse then lead to two definitions of continuity. Al-shami [6][7][8], defined and studied new generalization of open set. Taha [17], introduced and studied the concepts of r-fuzzy -open, r-fuzzy semi--open, r-fuzzy α--open and r-fuzzy β--open sets in a fuzzy ideal topological space (X, τ, ).…”

Section: Introductionmentioning

confidence: 99%

r-fuzzy δ-ℓ-open sets and fuzzy upper (lower) δ-ℓ-continuity via fuzzy idealization

Taha¹

2021

J. Math. Computer Sci.

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In this study, the concepts of r-fuzzy δ--open and r-fuzzy strong β--open sets are defined in a fuzzy ideal topological space (X, τ, ) based on the sense ofŠostak. Some properties of these sets along with their mutual relationships are discussed with the help of examples. Also, the concepts of fuzzy upper and lower δ--continuous (resp. strong β--continuous) multifunctions are introduced and studied. Moreover, the decomposition of fuzzy upper (resp. lower) semi--continuity and the decomposition of fuzzy upper (resp. lower) α--continuity are obtained. Finally, we constructed a new form of r-fuzzy connected set called r-fuzzy -connected and studied some of its properties via fuzzy ideals.

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More notions and mappings via somewhere dense sets

Cited by 19 publications

References 10 publications

Functionally Separation Axioms on General Topology

Functionally Separation Axioms on General Topology

Topological Approaches for Rough Continuous Functions with Applications

r-fuzzy δ-ℓ-open sets and fuzzy upper (lower) δ-ℓ-continuity via fuzzy idealization

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