Ψ-I-CLOSED SET, WEAKLY Ψ-I-CLOSED SET AND CONTRA Ψ-I-CONTINUOUS MAPPING IN IDEAL TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (8) ◽  
pp. 5745-5757
Author(s):  
C. Indirani ◽  
K. Meenambika
Keyword(s):  
Continuous Mapping ◽  
Topological Spaces ◽  
Closed Set

scholarly journals On Strongly b − θ -Continuous Mappings in Fuzzifying Topology

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Ting Yang ◽  
Ahmed Mostafa Khalil
Keyword(s):  
Fuzzy Logic ◽  
Continuous Mapping ◽  
Topological Spaces ◽  
Closed Set ◽  
Open Set ◽  
Neighborhood System ◽  
Continuous Mappings ◽  
Derived Set ◽  
New Type

In this article, we will define the new notions (e.g., b − θ -neighborhood system of point, b − θ -closure (interior) of a set, and b − θ -closed (open) set) based on fuzzy logic (i.e., fuzzifying topology). Then, we will explain the interesting properties of the above five notions in detail. Several basic results (for instance, Definition 7, Theorem 3 (iii), (v), and (vi), Theorem 5, Theorem 9, and Theorem 4.6) in classical topology are generalized in fuzzy logic. In addition to, we will show that every fuzzifying b − θ -closed set is fuzzifying γ -closed set (by Theorem 3 (vi)). Further, we will study the notion of fuzzifying b − θ -derived set and fuzzifying b − θ -boundary set and discuss several of their fundamental basic relations and properties. Also, we will present a new type of fuzzifying strongly b − θ -continuous mapping between two fuzzifying topological spaces. Finally, several characterizations of fuzzifying strongly b − θ -continuous mapping, fuzzifying strongly b − θ -irresolute mapping, and fuzzifying weakly b − θ -irresolute mapping along with different conditions for their existence are obtained.

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.

REFLEXIVITY INDEX AND IRRATIONAL ROTATIONS

2021 ◽  
pp. 1-13
Author(s):  
BINGZHANG MA ◽  
K. J. HARRISON
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Irrational Rotations ◽  
Index 2

Abstract We determine the reflexivity index of some closed set lattices by constructing maps relative to irrational rotations. For example, various nests of closed balls and some topological spaces, such as even-dimensional spheres and a wedge of two circles, have reflexivity index 2. We also show that a connected double of spheres has reflexivity index at most 2.

Four-Dimension Equivalences

1968 ◽  
Vol 20 ◽  
pp. 48-50 ◽  
Author(s):  
J. R. Gard ◽  
R. D. Johnson
Keyword(s):  
Topological Spaces ◽  
Covering Dimension ◽  
Closed Set ◽  
Set Separation

The object of this paper is to establish the equivalence of four functionrelated dimension concepts in arbitrary topological spaces. These concepts involve stability of functions (3, p. 74), the modification of covering dimension involving basic covers (1, p. 243) (which is equivalent to Yu. M. Smirnov's definition using normal covers), the definition involving essential mappings (2, p. 496), and a modification of the closed set separation characterization of dimension in (3, p. 35).

scholarly journals Forward analysis for WSTS, part I: completions

2020 ◽  
Vol 30 (7) ◽  
pp. 752-832
Author(s):  
Alain Finkel ◽  
Jean Goubault-Larrecq
Keyword(s):  
Transition System ◽  
Topological Spaces ◽  
Closed Set ◽  
Rich Family ◽  
Forward Analysis ◽  
Downward Closure

AbstractWe define representations for downward-closed subsets of a rich family of well-quasi-orders, and more generally for closed subsets of an even richer family of Noetherian topological spaces. This includes the cases of finite words, of multisets, of finite trees, notably. Those representations are given as finite unions of ideals, or more generally of irreducible closed subsets. All the representations we explore are computable, in the sense that we exhibit algorithms that decide inclusion, and compute finite unions and finite intersections. The origin of this work lies in the need for computing finite representations of sets of successors of the downward closure of one state, or more generally of a downward-closed set of states, in a well-structured transition system, and this is where we start: we define adequate notions of completions of well-quasi-orders, and more generally, of Noetherian spaces. For verification purposes, we argue that the required completions must be ideal completions, or more generally sobrifications, that is, spaces of irreducible closed subsets.

scholarly journals Some Features of Intuitionistic L- R1 Spaces

2018 ◽  
Vol 10 (1) ◽  
pp. 1-9
Author(s):  
R. Islam ◽  
M. S. Hossain
Keyword(s):  
Continuous Mapping ◽  
Topological Spaces ◽  
Hereditary Property

In this paper, we have introduced four notions of R1 space in intuitionistic L-topological spaces and established some implications among them. We have also proved that all of these definitions satisfy “good extension” and “hereditary” property. Finally, it has been shown that all concepts are preserved under one-one, onto and continuous mapping.

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