Two Forms of Pairwise Lindelöfness and Some Results Related to Hereditary Class in a Bigeneralized Topological Space

2017 ◽  
Vol 13 (02) ◽  
pp. 181-193 ◽  
Author(s):  
Santanu Acharjee ◽  
Binod Chandra Tripathy ◽  
Kyriakos Papadopoulos
Keyword(s):  
Topological Space ◽  
Hereditary Class ◽  
Equivalent Conditions

Bigeneralized topology was introduced in 2010. In this paper, we aim to contribute in the development of this area by proving results with respect to the hereditary class that defines two types of Lindelöf spaces in a bigeneralized topological space (BGTS). Some results on strong BGTS (briefly SBGTS) are proved by defining a [Formula: see text]-perfect mapping. We also prove some equivalent conditions with respect to the hereditary class.

scholarly journals A new convergence inducing the SI-topology

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6017-6029 ◽  
Author(s):  
Hadrian Andradi ◽  
Chong Shen ◽  
Weng Ho ◽  
Dongsheng Zhao
Keyword(s):  
Topological Space ◽  
Domain Theory ◽  
Scott Topology ◽  
Convergence Structure ◽  
Equivalent Conditions

In their attempt to develop domain theory in situ T0 spaces, Zhao and Ho introduced a new topology defined by irreducible sets of a resident topological space, called the SI-topology. Notably, the SI-topology of the Alexandroff topology of posets is exactly the Scott topology, and so the SI-topology can be seen as a generalisation of the Scott topology in the context of general T0 spaces. It is well known that the convergence structure that induces the Scott topology is the Scott-convergence - also known as lim-inf convergence by some authors. Till now, it is not known which convergence structure induces the SI-topology of a given T0 space. In this paper, we fill in this gap in the literature by providing a convergence structure, called the SI-convergence structure, that induces the SI-topology. Additionally, we introduce the notion of I-continuity that is closely related to the SI-convergence structure, but distinct from the existing notion of SI-continuity (introduced by Zhao and Ho earlier). For SI-continuity, we obtain here some equivalent conditions for it. Finally, we give some examples of non-Alexandroff SI-continuous spaces.

µ-Generalized closed sets via hereditary class in generalized topological space

2020 ◽  
Vol 33 (03) ◽  
Author(s):  
MANJEET SINGH ◽  
◽  
ASHA GUPTA ◽  
Keyword(s):  
Topological Space ◽  
Closed Sets ◽  
Hereditary Class ◽  
Generalized Topological Space

scholarly journals Soft Semi Local Functions in Soft Ideal Topological Spaces

2019 ◽  
Vol 12 (3) ◽  
pp. 857-869
Author(s):  
Fatouh Gharib ◽  
Alaa Mohamed Abd El-latif
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Local Function ◽  
Soft Sets ◽  
Soft Topology ◽  
Local Functions ◽  
Equivalent Conditions

In this paper, we define a soft semi local function (F, E) ∗s ( ˜I, τ ) by using semi open soft sets in a soft ideal topological space (X, τ, E, ˜I). This concept is discussed with a view to find new soft topologies from the original one, called ∗s-soft topology. Some properties and characterizations of soft semi local function are explored. Finally, the notion of soft semi compatibility of soft ideals with soft topologies is introduced and some equivalent conditions concerning this topic are established here.

ON SOME TYPES OF FUZZY ROUGH $\widehat{p}g$-KERNAL SETS IN FUZZY ROUGH TOPOLOGICAL SPACE

2020 ◽  
Vol 9 (3) ◽  
pp. 1421-1431
Author(s):  
S. Padmapriya ◽  
V. Naveena
Keyword(s):  
Topological Space

The Spatial Dimensions of Social Networks

2020 ◽  
pp. 367-383
Author(s):  
Zachary P. Neal
Keyword(s):  
Social Networks ◽  
Topological Space ◽  
Network Science ◽  
Spatial Dimensions

The first law of geography holds that everything is related to everything else, but near things are more related than distant things, where distance refers to topographical space. If a first law of network science exists, it would similarly hold that everything is related to everything else, but near things are more related than distant things, but where distance refers to topological space. Frequently these two laws collide, together holding that everything is related to everything else, but topographically and topologically near things are more related than topographically and topologically distant things. The focus of the spatial study of social networks lies in exploring a series of questions embedded in this combined law of geography and networks. This chapter explores the questions that have been asked and the answers that have been offered at the intersection of geography and networks.

scholarly journals Affine Subspaces of Curvature Functions from Closed Planar Curves

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese
Keyword(s):  
Arc Length ◽  
Planar Curves ◽  
Affine Subspaces ◽  
Planar Curve ◽  
Real Functions ◽  
Discrete Counterpart ◽  
Equivalent Conditions

AbstractGiven a pair of real functions (k, f), we study the conditions they must satisfy for $$k+\lambda f$$ k + λ f to be the curvature in the arc-length of a closed planar curve for all real $$\lambda $$ λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.

scholarly journals Quasi-ideal Ehresmann transversals: The spined product structure

2021 ◽  
Vol 19 (1) ◽  
pp. 77-86
Author(s):  
Xiangjun Kong ◽  
Pei Wang ◽  
Jian Tang
Keyword(s):  
Structure Theorem ◽  
Product Structure ◽  
Abundant Semigroup ◽  
Spined Product ◽  
Equivalent Conditions

Abstract In any U-abundant semigroup with an Ehresmann transversal, two significant components R and L are introduced in this paper and described by Green’s ∼ \sim -relations. Some interesting properties associated with R and L are explored and some equivalent conditions for the Ehresmann transversal to be a quasi-ideal are acquired. Finally, a spined product structure theorem is established for a U-abundant semigroup with a quasi-ideal Ehresmann transversal by means of R and L.

scholarly journals On $$\psi _{{\mathcal{H}}}( . )$$-operator in weak structure spaces with hereditary classes

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
H. M. Abu-Donia ◽  
Rodyna A. Hosny
Keyword(s):  
Topological Spaces ◽  
Structure Space ◽  
Hereditary Class ◽  
The Family ◽  
Main Target ◽  
Whole Space ◽  
Weak Structure

Abstract Weak structure space (briefly, wss) has master looks, when the whole space is not open, and these classes of subsets are not closed under arbitrary unions and finite intersections, which classify it from typical topology. Our main target of this article is to introduce $$\psi _{{\mathcal {H}}}(.)$$ ψ H ( . ) -operator in hereditary class weak structure space (briefly, $${\mathcal {H}}wss$$ H w s s ) $$(X, w, {\mathcal {H}})$$ ( X , w , H ) and examine a number of its characteristics. Additionally, we clarify some relations that are credible in topological spaces but cannot be realized in generalized ones. As a generalization of w-open sets and w-semiopen sets, certain new kind of sets in a weak structure space via $$\psi _{{\mathcal {H}}}(.)$$ ψ H ( . ) -operator called $$\psi _{{\mathcal {H}}}$$ ψ H -semiopen sets are introduced. We prove that the family of $$\psi _{{\mathcal {H}}}$$ ψ H -semiopen sets composes a supra-topology on X. In view of hereditary class $${\mathcal {H}}_{0}$$ H 0 , $$w T_{1}$$ w T 1 -axiom is formulated and also some of their features are investigated.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

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