scholarly journals Some Results via Gril Semi –p-Open Set

2021 ◽  
Vol 34 (4) ◽  
pp. 108-115
Author(s):  
Esmaeel R. B. ◽  
Shahadhuh N. M.
Keyword(s):  
Boundary Area ◽  
Lower Approximation ◽  
New Class ◽  
Open Set

The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

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.

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 Remarks on Pre-I-Regular Pre-I-Open Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
R. Sajuntha
Keyword(s):  
Equivalence Relation ◽  
Closed Sets ◽  
New Class ◽  
Fundamental Properties ◽  
Open Set ◽  
Regular Sets

We deal with the new class of pre-I-regular pre-I-open sets in which the notion of pre-I-open set is involved. We characterize these sets and study some of their fundamental properties. We also present other notions called extremally pre-I-disconnectedness, locally pre-I-indiscreetness, and pre-I-regular sets by utilizing the notion of pre-I-open and pre-I-closed sets by which we obtain some equivalence relation for pre-I-regular pre-I-open sets.

scholarly journals Scope for application of Topological spaces in Data Granulation through a new class of nearly open set Semi* Regular*- Open sets

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
Basari Kodi K , Et. al.
Keyword(s):  
Topological Spaces ◽  
New Class ◽  
Open Set ◽  
Regular Open

The purpose of this paper is to define and study a new class of weaker form of regular*-open sets called semi*- regular*- open sets in topological spaces. Finally we conclude with the scope of this new class of open sets in applications of Data granulation.  

Onintuitionistic fuzzy-I-open sets, intuitionistic fuzzy semi-I-open sets and a decomposition of intuitionistic fuzzy-I-continuity

2021 ◽  
Vol 7 (4) ◽  
Keyword(s):  
Topological Spaces ◽  
New Class ◽  
Intuitionistic Fuzzy ◽  
Open Set ◽  
Fuzzy Ideal

In this paper, we introduce a new class of intuitionistic fuzzy ideal open sets in intuitionistic fuzzy ideal topological spaces; intuitionistic fuzzy-I-open set and intuitionistic fuzzy semi-I-open set and given a decomposition of fuzzy continuity.

scholarly journals Beta- Star- Continuity and Beta- Star- Contra- Continuity

2021 ◽  
Vol 7 ◽  
pp. 43-66
Author(s):  
Raja Mohammad Latif
Keyword(s):  
Continuous Functions ◽  
General Topology ◽  
Topological Spaces ◽  
New Class ◽  
Fundamental Properties ◽  
Open Set ◽  
Class Of Functions

In 2014 Mubarki, Al-Rshudi, and Al- Juhani introduced and studied the notion of a set in general topology called β*-open set and investigated its fundamental properties and studied the relationships between β*-open set and other topological sets including β*-continuity in topological spaces. We introduce and investigate several properties and characterizations of a new class of functions between topological spaces called β*- open, β*- closed, β*- continuous and β*- irresolute functions in topological spaces. We also introduce slightly β*- continuous, totally β*- continuous and almost β*- continuous functions between topological spaces and establish several characterizations of these new forms of functions. Furthermore, we also introduce and investigate certain ramifications of contra continuous and allied functions, namely, contra β*- continuous, and almost contra β*-continuous functions along with their several properties, characterizations and natural relationships. Moreover, we introduce new types of closed graphs by using β*- open sets and investigate its properties and characterizations in topological spaces.

scholarly journals is*-Open Sets, is*- Mappings and is*-separation Axioms in Topological Spaces

2019 ◽  
Author(s):  
Omar Khattabomar
Keyword(s):  
Topological Spaces ◽  
New Class ◽  
Open Set ◽  
Separation Axioms ◽  
Continuous Mappings

In this paper, we introduce a new class of open sets that is called is*-open set . Also, we present the notion of is*-continuous, is*-open, is*-irresolute, is*-totally continuous, and is-contra-continuous mappings, and we investigate some properties of these mappings. Furthermore, we introduce some is*-separation axioms, and is*-mappings are related with is*-separation axioms. . .

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 ON G-OPEN SET

2007 ◽  
Vol 4 (3) ◽  
pp. 482-484
Author(s):  
Baghdad Science Journal
Keyword(s):  
Topological Space ◽  
New Class ◽  
Open Set

A new class of generalized open sets in a topological space, called G-open sets, is introduced and studied. This class contains all semi-open, preopen, b-open and semi-preopen sets. It is proved that the topology generated by G-open sets contains the topology generated by preopen,b-open and semi-preopen sets respectively.

The observation of solutions in Ni3Nb

1988 ◽  
Vol 46 ◽  
pp. 540-541
Author(s):  
Z.M. Wang ◽  
J.P. Zhang
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Phase Modulation ◽  
High Resolution Electron Microscopy ◽  
Antiphase Domain ◽  
Boundary Area ◽  
Matrix Type ◽  
Resolution Electron ◽  
Domain Boundaries ◽  
Kontorova Model

High resolution electron microscopy reveals that antiphase domain boundaries in β-Ni3Nb have a hexagonal unit cell with lattice parameters ah=aβ and ch=bβ, where aβ and bβ are of the orthogonal β matrix. (See Figure 1.) Some of these boundaries can creep “upstairs” leaving an incoherent area, as shown in region P. When the stepped boundaries meet each other, they do not lose their own character. Our consideration in this work is to estimate the influnce of the natural misfit δ{(ab-aβ)/aβ≠0}. Defining the displacement field at the boundary as a phase modulation Φ(x), following the Frenkel-Kontorova model [2], we consider the boundary area to be made up of a two unit chain, the upper portion of which can move and the lower portion of the β matrix type, assumed to be fixed. (See the schematic pattern in Figure 2(a)).

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