scholarly journals Generalized semi-open sets via ideals in topological space

2021 ◽  
Vol 29 (2) ◽  
pp. 231-236
Author(s):  
RITU SEN
Keyword(s):  
Topological Space ◽  
New Type

In this paper we have introduced a new type of sets termed as µˆ-open sets which unifies semiopen sets and discussed some of its properties. We have also introduced another type of weak open sets termed as Iµˆ -open sets depending on a GT as well as an ideal on a topological space. Finally the concept of weakly Iτˆ -open sets are investigated.

Star Neutrosophic Fuzzy Topological Space

2020 ◽  
pp. 77-82
Author(s):  
A.A A.A.Salama ◽  
◽  
◽  
◽  
Hewayda ElGhawalby ◽  
...  
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
New Type

In this paper, we aim to develop a new type of neutrosophic fuzzy set called the star neutrosophic fuzzy set as a generalization to star neutrosophic crisp set defined in by Salama et al.[8], and study some of its properties. Adedd to, we introduce the notion of star neutrosophic fuzzy topological space as a generalization to some topological consepts as star neutrosophic fuzzy closure, and star neutrosophic fuzzy interior. Finally, we extend the concepts of fuzzy topological space, and intuitionistic fuzzy topological space to the case of star neutrosophic fuzzy sets.

scholarly journals On generalized γµ-closed sets and related continuity

2021 ◽  
Vol 13 (2) ◽  
pp. 483-493
Author(s):  
Ritu Sen
Keyword(s):  
Topological Space ◽  
Main Interest ◽  
Closed Sets ◽  
Separation Axioms ◽  
Preservation Theorems ◽  
Generalized Topological Space ◽  
New Type ◽  
Weak Separation

Abstract In this paper our main interest is to introduce a new type of generalized open sets defined in terms of an operation on a generalized topological space. We have studied some properties of this newly defined sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have studied some preservation theorems in terms of some irresolute functions.

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

scholarly journals Theory of g-Tg-Connectedness

2018 ◽  
Author(s):  
Mohammad Irshad Khodabocus ◽  
Noor-Ul-Hacq Sookia
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Starting Point ◽  
Generalized Topological Space ◽  
New Type

Several specific types of ordinary and generalized connectedness in a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new type of generalized connectedness in a generalized topological space is reported herein as a starting point for more generalized types.

scholarly journals Hyperconnectedness modulo an ideal

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6375-6386
Author(s):  
B.K. Tyagi ◽  
Manoj Bhardwaj ◽  
Sumit Singh
Keyword(s):  
Topological Space ◽  
New Type

In this paper, hyperconnectedness with respect to an ideal, called hyperconnectedness modulo an ideal, of a topological space X is introduced. It is shown that hyperconnectedness and hyperconnectedness modulo an ideal coincide in case of trivial and codense ideal. Several characterisations of hyperconnectedness modulo an ideal I are obtained using semi-open, pre-open and semi-preopen sets. It is also shown that I-hyperconnectedness and hyperconnectedness modulo I, where I is an ideal in a space X, are equivalent. A new type of semi-open modulo ideal sets are defined and several characterisations of hyperconnectedness modulo an ideal using these sets are obtained.

scholarly journals Pre Separation Axioms In Neutrosophic Crisp Topological Spaces

2020 ◽  
pp. 72-79
Author(s):  
Riad K. Al Al-Hamido ◽  
◽  
◽  
◽  
Luai Salha ◽  
...  
Keyword(s):  
Topological Space ◽  
The Other ◽  
Topological Spaces ◽  
Open Set ◽  
Separation Axioms ◽  
New Type

In this paper, A new type of separation axioms in the neutrosophic crisp Topological space named neutrosophic crisp pre separation axioms is going to be defined , in which neutrosophic crisp pre open set and neutrosophic crisp point are to be depended on. Also, relations among them and the other type are going to be found.

scholarly journals A NEW TYPE OF CLUSTER SETS AND ITS APPLICATIONS

1995 ◽  
Vol 26 (4) ◽  
pp. 327-336
Author(s):  
M. N. MUKHERJEE ◽  
S. RAYCHAUDHURI
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Cluster Sets ◽  
New Type ◽  
Func Tion

In this paper we introduce the concept of a new type of cluster sets, termed $\delta$-cluster sets, of functions and multifunctions between topological spaces. Expressions of such sets are found and multifunctions with $\delta$-closed graphs are characterized. Also the behaviour of $\delta$-cluster sets toward a-continuity of a func- tion is observed. Finally as applications, we find new characterizations of almost regularity, near compactness and near Lindelofness of a topological space in terms of $\delta$-cluster sets of suitable multifunctions.

scholarly journals Lacunary distributional convergence in topological spaces

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4297-4306
Author(s):  
Havva Uluçay ◽  
Mehmet Ünver
Keyword(s):  
Topological Space ◽  
Group Structure ◽  
Lacunary Sequence ◽  
Distribution Functions ◽  
Topological Spaces ◽  
Hausdorff Topological Space ◽  
Lacunary Sequences ◽  
Summability Methods ◽  
Borel Field ◽  
New Type

Most of the summability methods cannot be defined in an arbitrary Hausdorff topological space unless one introduces a linear or a group structure. In the present paper, using distribution functions over the Borel ?-field of the topology and lacunary sequences we define a new type of convergencemethod in an arbitrary Hausdorff topological space and we study some inclusion theorems with respect to the resulting summability method. We also investigate the inclusion relation between lacunary sequence and lacunary refinement of it.

scholarly journals Λ-Ib-Sets in Topological Space

2019 ◽  
pp. 71-74
Author(s):  
Carlos Andres Granados Ortiz
Keyword(s):  
Topological Space ◽  
The Other ◽  
Other Hand ◽  
New Type ◽  
Definition Of

In this paper we studied a new type of sets that called Λ-Ib-sets, for planting this sets it was necessary to know about b-opens sets were introduced by [4], b-I-opens sets were introduced by [2] and the notion of ideal in topological space was defined by [5], thus we used those concepts and created the sets which were studied, furthermore we studied relationship between Λ-I sets and Λ-Is sets, in fact some properties were planted, on the other hand, the definition of continuity from Λ-Ib-sets was added and some examples are shown.

The Ra operator in ideal topological spaces

2016 ◽  
Vol 25 (1) ◽  
pp. 1-10
Author(s):  
WADEI FARIS AL-OMERI ◽  
◽  
MOHD. SALMI MD. NOORANI ◽  
T. NOIRI ◽  
A. AL-OMARI ◽  
...  
Keyword(s):  
Topological Space ◽  
Ideal Space ◽  
Topological Spaces ◽  
Local Function ◽  
New Type ◽  
The Ideal

Given a topological space (X, τ) an ideal I on X and A ⊆ X, the concept of a-local function is defined as follows Aa ∗ (I, τ) = {x ∈X : U ∩ A /∈ I, for every U ∈ τ a(x)}. In this paper a new type of space has been introduced with the help of a-open sets and the ideal topological space called a-ideal space. We introduce an operator <a : ℘(X) → τ, for every A ∈ ℘(X), and we use it to define some interesting generalized a-open sets and study their properties.

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