scholarly journals η-Open Sets in Topological Spaces

2019 ◽  
Vol 8 (10S) ◽  
pp. 276-282
Keyword(s):  
Topological Space ◽  
The Other ◽  
Topological Spaces ◽  
New Class ◽  
Relationship Of

In this paper a new class of open sets in a topological space called η-open sets is defined and the inclusive relationship of this set with the other existing sets like semi open, pre-open, α-open, r-open sets are discussed.In addition to this the concept of η-interior, η-closure, η-boundary, η-exterior, η-derived, η-border, η-neighbourhood, η-dense, η-residual are also introduced.

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 Theory of g-Tg-Interior and g-Tg-Closure Operators: Definitions, Essential Properties, and Commutativity

2019 ◽  
Author(s):  
Mohammad Irshad KHODABOCUS ◽  
Noor-Ul-Hacq SOOKIA
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closure Operators ◽  
New Class ◽  
Essential Properties ◽  
Generalized Topological Space ◽  
Outstanding Result

In a generalized topological space Tg = (Ω, Tg), ordinary interior and ordinary closure operators intg, clg : P (Ω) −→ P (Ω), respectively, are defined in terms of ordinary sets. In order to let these operators be as general and unified a manner as possible, and so to prove as many generalized forms of some of the most important theorems in generalized topological spaces as possible, thereby attaining desirable and interesting results, the present au- thors have defined the notions of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in terms of a new class of generalized sets which they studied earlier and studied their essen- tial properties and commutativity. The outstanding result to which the study has led to is: g-Intg : P (Ω) −→ P (Ω) is finer (or, larger, stronger) than intg : P (Ω) −→ P (Ω) and g-Clg : P (Ω) −→ P (Ω) is coarser (or, smal ler, weaker) than clg : P (Ω) −→ P (Ω). The elements supporting this fact are reported therein as a source of inspiration for more generalized operations.

scholarly journals A Class of Separation Axioms in Generalized Topology

2016 ◽  
Vol 4 (2) ◽  
pp. 151-159
Author(s):  
D Anabalan ◽  
Santhi C
Keyword(s):  
Topological Space ◽  
Generalized Topology ◽  
Regular Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
New Class ◽  
Separation Axioms ◽  
Generalized Topological Space

The purpose of this paper is to introduce and study some new class of definitions like µ-point closure and gµ –regular space concerning generalized topological space. We obtain some characterizations and several properties of such definitions. This paper takes some investigations on generalized topological spaces with gµ –closed sets and gµ–closed sets.

scholarly journals Weakly b-Closed Sets and Weakly b-Open Sets based of Fuzzy Neutrosophic bi-Topological Spaces

2020 ◽  
pp. 34-43
Author(s):  
Fatimah M. .. ◽  
◽  
◽  
Sarah W. Raheem
Keyword(s):  
The Other ◽  
Topological Spaces ◽  
Neutrosophic Sets ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Other Hand ◽  
Definition Of

In this paper, we present and study some of the basic properties of the new class of sets called weakly b-closed sets and weakly b- open sets in fuzzy neutrosophic bi-topological spaces. We referred to some results related to the new definitions, which we taked the case of equal in the definition of b-sets instead of subset. Then, we discussed the relations between the new defined sets by hand and others fuzzy neutrosophic sets which were studied before us on the other hand on fuzzy neutrosophic bi-topological spaces. Then, we have studied some of characteristics and some relations are compared with necessary examples.

scholarly journals Theory of g-Tg-Maps

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

Several specific types of generalized maps of 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 class of generalized maps of a generalized topological space is reported herein as a starting point for more generalized classes.

scholarly journals Theory of g-Tg-Compactness

2019 ◽  
Author(s):  
Mohammad Irshad Khodabocus ◽  
Noor-Ul-Hacq Sookia
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
New Class ◽  
Starting Point ◽  
Generalized Topological Space ◽  
Generalized Classes

Several specific types of generalized compactness of generalized topological spaces have been defined, investigated and related to compactness in ordinary topological spaces from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized compactness in a generalized topological space is reported herein as a starting point for more generalized classes.

scholarly journals Tilings in topological spaces

1999 ◽  
Vol 22 (3) ◽  
pp. 611-616 ◽  
Author(s):  
F. G. Arenas
Keyword(s):  
Topological Space ◽  
Pairwise Disjoint ◽  
The Other ◽  
Vector Spaces ◽  
Topological Spaces ◽  
Topological Vector Spaces ◽  
Other Hand ◽  
Extensive Bibliography

Atilingof a topological spaceXis a covering ofXby sets (calledtiles) which are the closures of their pairwise-disjoint interiors. Tilings ofℝ2have received considerable attention (see [2] for a wealth of interesting examples and results as well as an extensive bibliography). On the other hand, the study of tilings of general topological spaces is just beginning (see [1, 3, 4, 6]). We give some generalizations for topological spaces of some results known for certain classes of tilings of topological vector spaces.

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 Fuzzy Semi Pre Homeomorphism in Fuzzy Topological Spaces

2020 ◽  
Vol 33 (4) ◽  
pp. 73
Author(s):  
Saleem Y. Majeed
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
New Class ◽  
Fuzzy Function ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Class Of Functions

   The aim of this paper is to introduce and study new class of fuzzy function called fuzzy semi pre homeomorphism in a fuzzy topological space by utilizing fuzzy semi pre-open sets. Therefore, some of their characterization has been proved; In addition to that we define, study and develop corresponding to new class of fuzzy semi pre homeomorphism in fuzzy topological spaces using this new class of functions.

scholarly journals A New Class on Ng# α-Quotient Mappings in Nano Topological Space

2020 ◽  
Vol 12 (3) ◽  
pp. 269-277
Author(s):  
V. Kokilavani ◽  
S. Visagapriya
Keyword(s):  
Topological Space ◽  
Quotient Mapping ◽  
New Class ◽  
Quotient Mappings ◽  
Relationship Of

The primary intend of this article is to define a new class of mappings called Ng# α-quotient mappings in nano topological space. The intention is to analyze characterizations and inter relationship of Ng# α-quotient mappings with nano Tg#α-space, Ng# α-continuous, Ng# α-open, Ng# α-irresolute, Ng# α-homeomorphism and nano α-quotient mapping. Also several properties of strongly Ng# α-quotient mapping are derived and the relationships among them are illustrated with the help of examples. Their interesting composition with strongly Ng# α-irresolute are established. The concept of Ng# α-quotient mapping is explored and composition of mappings under strongly Ng# α-quotient mapping and Ng# α-quotient mapping are discussed. Furthermore, to emphasize Ng# α-quotient mapping a few examples are considered and derived in detail.

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