scholarly journals Neutrosophic soft δ-topology and neutrosophic soft δ-compactness

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3441-3458
Author(s):  
Ahu Acikgoz ◽  
Ferhat Esenbel
Keyword(s):  
Basic Properties ◽  
Soft Topology ◽  
Open Set ◽  
Continuous Mappings ◽  
Regular Open

We introduce the concepts of neutrosophic soft ?-interior, neutrosophic soft quasi-coincidence, neutrosophic soft q-neighbourhood, neutrosophic soft regular open set, neutrosophic soft ?-closure, neutrosophic soft ?-closure and neutrosophic soft semi open set. It is also shown that the set of all neutrosophic soft ?-open sets is a neutrosophic soft topology, which is called the neutrosophic soft ?-topology. We obtain equivalent forms of neutrosophic soft ?-continuity. Moreover, the notions of neutrosophic soft ?-compactness and neutrosophic soft locally ?-compactness are defined and their basic properties under neutrosophic soft ?-continuous mappings are investigated.

scholarly journals ON An Infra-\(\alpha\)-Open Sets

2016 ◽  
Vol 4 (3) ◽  
pp. 12
Author(s):  
Hakeem Othman ◽  
Md.Hanif. Page
Keyword(s):  
General Topology ◽  
Connected Space ◽  
Basic Properties ◽  
New Class ◽  
Fundamental Properties ◽  
Open Set ◽  
Continuous Mappings

<p>In this paper, we define a new class of set in general topology called an infra- \(\alpha\) open set and we investigate fundamental properties by using this new class. The relation between infra-\(\alpha\)-open set and other topological sets are studied.</p><p>Moreover, In the light of this new definition, we also define some generalization of continuous mappings and discuss the relations between these new classes of mappings and other continuous mappings. Basic properties of these new mappings are studied and we apply these new classes to give characterization of connected space.</p>

scholarly journals Some New Properties of Fuzzy Maximal Regular Open Sets

2020 ◽  
Vol 7 ◽  
Keyword(s):  
Topological Space ◽  
Open Subset ◽  
Basic Properties ◽  
Fundamental Properties ◽  
Properties And Characterization ◽  
Open Set ◽  
Fuzzy Topological Space ◽  
Regular Open ◽  
Characterization Theorems ◽  
Decomposition Theorems

A proper nonempty open subset of a fuzzy topological space is said to be a fuzzy maximal regular open set , if any regular open set which contains is or . The purpose of this paper is to study some new fundamental properties of fuzzy maximal regular open sets. The decomposition theorems for a fuzzy maximal regular open set are investigated. Notion and basic properties of radical of fuzzy maximal regular open sets are established, such as the law of fuzzy radical closure. Some new properties and characterization theorems of fuzzy maximal regular open set are achieved.

scholarly journals Soft ditopological spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 209-222 ◽  
Author(s):  
Tugbahan Dizman ◽  
Alexander Sostak ◽  
Saziye Yuksel
Keyword(s):  
Fuzzy Sets ◽  
Soft Set ◽  
Fuzzy Topology ◽  
Basic Properties ◽  
Soft Topology ◽  
Continuous Mappings ◽  
Basic Concepts

We introduce the concept of a soft ditopological space as the "soft Generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Ert?rk, ?. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147 (2) (2004), 171-199. Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology. The first one is used to describe openness-type properties of a space while the second one deals with its closedness-type properties. We study basic properties of such spaces and accordingly defined continuous mappings between such spaces.

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

scholarly journals Some properties of maximal open sets

2003 ◽  
Vol 2003 (21) ◽  
pp. 1331-1340 ◽  
Author(s):  
Fumie Nakaoka ◽  
Nobuyuki Oda
Keyword(s):  
Decomposition Theorem ◽  
Basic Properties ◽  
Fundamental Properties ◽  
Open Set ◽  
The Law

Some fundamental properties of maximal open sets are obtained, such as decomposition theorem for a maximal open set. Basic properties of intersections of maximal open sets are established, such as the law of radical closure.

scholarly journals Almost-continuous path connected spaces

1981 ◽  
Vol 4 (4) ◽  
pp. 823-825
Author(s):  
Larry L. Herrington ◽  
Paul E. Long
Keyword(s):  
Continuous Function ◽  
Connected Components ◽  
Continuous Path ◽  
Open Set ◽  
Regular Open ◽  
Path Connected ◽  
Almost Continuous ◽  
Connected Spaces

M. K. Singal and Asha Rani Singal have defined an almost-continuous functionf:X→Yto be one in which for eachx∈Xand each regular-open setVcontainingf(x), there exists an openUcontainingxsuch thatf(U)⊂V. A spaceYmay now be defined to be almost-continuous path connected if for eachy0,y1∈Ythere exists an almost-continuousf:I→Ysuch thatf(0)=y0andf(1)=y1An investigation of these spaces is made culminating in a theorem showing when the almost-continuous path connected components coincide with the usual components ofY.

A View on Fuzzy Minimal Open Sets and Fuzzy Maximal Open Sets

2015 ◽  
Vol 7 (1) ◽  
pp. 62-73 ◽  
Author(s):  
Hamid Reza Moradi
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Class ◽  
Properties And Characterization ◽  
Open Set ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Characterization Theorems

A nonzero fuzzy open set () of a fuzzy topological space is said to be fuzzy minimal open (resp. fuzzy maximal open) set if any fuzzy open set which is contained (resp. contains) in is either or itself (resp. either or itself). In this note, a new class of sets called fuzzy minimal open sets and fuzzy maximal open sets in fuzzy topological spaces are introduced and studied which are subclasses of open sets. Some basic properties and characterization theorems are also to be investigated.

scholarly journals Continuity in fuzzy bitopological ordered spaces

2021 ◽  
Vol 40 (3) ◽  
pp. 681-696
Author(s):  
Runu Dhar
Keyword(s):  
Basic Properties ◽  
Properties And Characterization ◽  
Continuous Mappings ◽  
Characterization Theorems ◽  
Closed Mappings

The aim of the present paper is to introduce and study different forms of continuity in fuzzy bitopological ordered spaces. The concepts of different mappings such as pairwise fuzzy I -continuous mappings, pairwise fuzzy D -continuous mappings, pairwise fuzzy B -continuous mappings, pairwise fuzzy I -open mappings, pairwise fuzzy D -open mappings, pairwise fuzzy B -open mappings, pairwise fuzzy I -closed mappings, pairwise fuzzy D -closed mappings and pairwise fuzzy B -closed mappings have been introduced. Some of the basic properties and characterization theorems of these mappings have been investigated.

scholarly journals Infra Soft Semiopen Sets and Infra Soft Semicontinuity

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Tareq M. Al-shami ◽  
A. A. Azzam
Keyword(s):  
Soft Set ◽  
Finite Product ◽  
Finite Intersection ◽  
Soft Topology ◽  
Continuous Mappings

To contribute to the area of infra soft topology, we introduce one of the generalizations of infra soft open sets called infra soft semiopen sets. We establish some characterizations of them and study their main properties. We determine under what condition this class is closed under finite intersection and show that this class is preserved under infra soft continuous mappings and finite product of soft spaces. Then, we present the concepts of infra semi-interior, infra semiclosure, infra semilimit, and infra semiboundary soft points of a soft set and elucidate the relationships between them. Finally, we exploit infra soft semiopen and infra soft semiclosed sets to define new types of soft mappings. We characterize each one of these soft mappings and explore main features.

HOMOGENIZATION OF ENERGIES DEFINED ON PAIRS SET-FUNCTION

2009 ◽  
Vol 11 (03) ◽  
pp. 459-479 ◽  
Author(s):  
MARGHERITA SOLCI
Keyword(s):  
Asymptotic Behavior ◽  
Energy Density ◽  
Convergence Result ◽  
Energy Scale ◽  
Surface Energy Density ◽  
Surface Energies ◽  
Open Set ◽  
Γ Convergence ◽  
Regular Open ◽  
Set Function

In the present work, we deal with the problem of the asymptotic behavior of a sequence of non-homogeneous energies depending on a pair set-function of the form [Formula: see text] with u ∈ H1(Ω), E regular open set and the energy densities f and φ both 1-periodic in the first variable; this leads, in the Γ-limit, to a problem of homogenization. We prove a Γ-convergence result for the sequence {Fε}, showing that there is no interaction between the homogenized bulk and surface energy density; that is, even though the effect of the bulk and surface energies are at the same energy scale, oscillations in the bulk term can be neglected close to the surfaces ∂*E and S(u), where surface oscillations are dominant.

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