Closure, Interior and Compactness in Ordinary Smooth Topological Spaces

Lee, Jeong Gon; Hur, Kyeong; Lim, Pyung Ki

doi:10.5391/ijfis.2014.14.3.231

Cited by 6 publications

(3 citation statements)

References 11 publications

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“…As a consequence of these definitions we reduce the additional hypotheses in the results of [1] and also generalize several properties of the types of compactness in [1].…”

Section: Introductionmentioning

confidence: 90%

“…In particular, Chae et al [10] studied the set OST(X) of all ordinary smooth topologies on X in the sense of a lattice. Moreover, Lim et al [1] introduced and investigated closures, interiors and the types of compactness in ordinary smooth topological spaces. However the results obtained include additional conditions since the ordinary smooth closure and ordinary smooth interior defined there do not have such nice properties as the closure and interior operators in a classical topological space.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces

Lee¹,

Lim²,

Hur³

2013

Journal of Korean Institute of Intelligent Systems

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We give a new definition of ordinary smooth closure and ordinary smooth interior of an ordinary subset in an ordinary smooth topological space which have almost all the properties of the corresponding operators in a classical topological space. As a consequence of these definitions we reduce the additional hypotheses in the results of [1] and also generalize several properties of the types of compactness in [1].

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“…As a consequence of these definitions we reduce the additional hypotheses in the results of [1] and also generalize several properties of the types of compactness in [1].…”

Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces

Lee¹,

Lim²,

Hur³

2013

Journal of Korean Institute of Intelligent Systems

Self Cite

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“…In 2012, Lim et al [34] studied general properties in ordinary smooth topological spaces. In addition, they [35][36][37] investigated closures, interiors and compactness in ordinary smooth topological spaces.…”

Section: Introductionmentioning

confidence: 99%

Ordinary Single Valued Neutrosophic Topological Spaces

et al. 2019

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We define an ordinary single valued neutrosophic topology and obtain some of its basicproperties. In addition, we introduce the concept of an ordinary single valued neutrosophic subspace.Next, we define the ordinary single valued neutrosophic neighborhood system and we show thatan ordinary single valued neutrosophic neighborhood system has the same properties in a classicalneighborhood system. Finally, we introduce the concepts of an ordinary single valued neutrosophicbase and an ordinary single valued neutrosophic subbase, and obtain two characterizations of anordinary single valued neutrosophic base and one characterization of an ordinary single valuedneutrosophic subbase.

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On Single-Valued Neutrosophic Ideals in Šostak Sense

2020

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Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion of single-valued neutrosophic ideals sets in Šostak’s sense, which is considered as a generalization of fuzzy ideals in Šostak’s sense and intuitionistic fuzzy ideals. The concept of single-valued neutrosophic ideal open local function is also introduced for a single-valued neutrosophic topological space. The basic structure, especially a basis for such generated single-valued neutrosophic topologies and several relations between different single-valued neutrosophic ideals and single-valued neutrosophic topologies, are also studied here. Finally, for the purpose of symmetry, we also define the so-called single-valued neutrosophic relations.

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Closure, Interior and Compactness in Ordinary Smooth Topological Spaces

Cited by 6 publications

References 11 publications

Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces

Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces

Ordinary Single Valued Neutrosophic Topological Spaces

On Single-Valued Neutrosophic Ideals in Šostak Sense

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