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.

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 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 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 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 "Some Relations On Fuzzy δ-Open Set in Fuzzy Topological Space on Fuzzy Set "

2020 ◽  
Vol 8 (1) ◽  
pp. 31-39
Author(s):  
Muner A. Alkhafaji ◽  
Dalia R. Abd
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Open Set ◽  
Fuzzy Topological Space

The aim of introduce and study the notion of a fuzzy δ-open set (Ω-open set, α− Ω-open set, feebly –open set, α-open set, ƥ-open set, Sp-open set, a-open set) and the relationships between them and fuzzy 𝛿-open set in fuzzy topological space on fuzzy set and some properties, remarks related to them .

scholarly journals Further properties of (γ, γ0 )-preopen sets

2012 ◽  
Vol 21 (1) ◽  
pp. 103-114
Author(s):  
N. RAJESH ◽  
◽  
V. VIJAYABHARATHI ◽  
Keyword(s):  
Topological Space ◽  
Fundamental Properties ◽  
Open Set

In [Carpintero, C., Rajesh, N. and Rosas, E., On a class of (γ, γ0 )-preopen sets in a topological space, Fasciculi Mathematici, 46 (2011), 25–36], the authors introduced the notion of (γ, γ0 )-preopeness and investigated its fundamental properties. In this paper, we investigate some more properties of this type of open set.

Characterization of Fuzzy δg*-Closed Sets in Fuzzy Topological Spaces

2016 ◽  
Vol 5 (2) ◽  
pp. 1-12
Author(s):  
Anahid Kamali ◽  
Hamid Reza Moradi
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Topological Spaces ◽  
Basic Properties ◽  
Closed Sets ◽  
Research Article ◽  
Classical Paper ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The purpose of this research article is to explain the meaning of g-closed sets in fuzzy topological spaces, which is more understandable to the readers and we find some of its basic properties. The concept of fuzzy sets was introduced by Zadeh in his classical paper (1965). Thereafter many investigations have been carried out, in the general theoretical field and also in different applied areas, based on this concept. The idea of fuzzy topological space was introduced by Chang (1968). The idea is more or less a generalization of ordinary topological spaces. Different aspects of such spaces have been developed, by several investigators. This paper is also devoted to the development of the theory of fuzzy topological spaces.

ON THE SPECTRALIFICATION OF A HEMISPECTRAL SPACE

2011 ◽  
Vol 10 (04) ◽  
pp. 687-699
Author(s):  
OTHMAN ECHI ◽  
MOHAMED OUELD ABDALLAHI
Keyword(s):  
Topological Space ◽  
Open Subset ◽  
Full Subcategory ◽  
Topological Spaces ◽  
Open Problems ◽  
Complete Answer ◽  
Reflective Subcategory ◽  
Continuous Map ◽  
Open Set ◽  
Spectral Spaces

An open subset U of a topological space X is called intersection compact open, or ICO, if for every compact open set Q of X, U ∩ Q is compact. A continuous map f of topological spaces will be called spectral if f-1 carries ICO sets to ICO sets. Call a topological space Xhemispectral, if the intersection of two ICO sets of X is an ICO. Let HSPEC be the category whose objects are hemispectral spaces and arrows spectral maps. Let SPEC be the full subcategory of HSPEC whose objects are spectral spaces. The main result of this paper proves that SPEC is a reflective subcategory of HSPEC. This gives a complete answer to Problem BST1 of "O. Echi, H. Marzougui and E. Salhi, Problems from the Bizerte–Sfax–Tunis seminar, in Open Problems in Topology II, ed. E. Pearl (Elsevier, 2007), pp. 669–674."

scholarly journals Some properties of weak form of $\gamma$-semi-open sets

2012 ◽  
Vol 43 (3) ◽  
pp. 329-338
Author(s):  
Sabir Hussain ◽  
Mohammad Ahmad Alghamdi
Keyword(s):  
Decomposition Theorem ◽  
Weak Form ◽  
Topological Spaces ◽  
Basic Properties ◽  
Fundamental Properties ◽  
Open Set

In this paper, we introduce and explore fundamental properties of weak form of $\gamma$-semi-open sets namely maximal $\gamma$-semi-open sets in topological spaces such as decomposition theorem for maximal $\gamma$-semi-open set. Basic properties of intersection of maximal $\gamma$-semi-open sets are established, such as the $\gamma$-semi-closure law of $\gamma$-semi-radical.

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>

Sign in / Sign up

Export Citation Format

Share Document