scholarly journals Some topology on zero-dimensional subrings of product of rings

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4589-4595
Author(s):  
Hassan Mouadi ◽  
Driss Karim
Keyword(s):  
Limit Point ◽  
Direct Limit ◽  
Zariski Topology ◽  
Basic Properties

Let R be a ring and {Ri}i?I a family of zero-dimensional rings. We define the Zariski topology on Z(R,?Ri) and study their basic properties. Moreover, we define a topology on Z(R,?Ri) by using ultrafilters; it is called the ultrafilter topology and we demonstrate that this topology is finer than the Zariski topology. We show that the ultrafilter limit point of a collections of subrings of Z(R,?Ri) is a zero-dimensional ring. Its relationship with F-lim and the direct limit of a family of rings are studied.

scholarly journals On I-statistically limit points and I-statistically cluster points of sequences of fuzzy numbers

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 140-147
Author(s):  
Binod Chandra Tripathy ◽  
Shyamal Debnath ◽  
Debjani Rakshit
Keyword(s):  
Limit Point ◽  
Fuzzy Numbers ◽  
Cluster Point ◽  
Basic Properties ◽  
Sequences Of Fuzzy Numbers ◽  
Limit Points ◽  
Cluster Points

The main aim of this paper is to introduce I-st limit points and I-st cluster points of a sequence of fuzzy numbers and also study some of its basic properties. Conditions for a I-st limit point of a I-st cluster point are investigated.

On the Essence and Tipology of International Public Goods

2005 ◽  
pp. 131-141
Author(s):  
V. Mortikov
Keyword(s):  
Economic Policy ◽  
Social Construction ◽  
Public Goods ◽  
Public Good ◽  
Global Public Goods ◽  
Club Goods ◽  
Basic Properties ◽  
International Public Goods ◽  
Regional Public Goods ◽  
Joint Products

The basic properties of international public goods are analyzed in the paper. Special attention is paid to the typology of international public goods: pure and impure, excludable and nonexcludable, club goods, regional public goods, joint products. The author argues that social construction of international public good depends on many factors, for example, government economic policy. Aggregation technologies in the supply of global public goods are examined.

The advancement of silicon-on-insulator (SOI) devices and their basic properties

2020 ◽  
Vol 23 (3) ◽  
pp. 227-252
Author(s):  
T.E. Rudenko ◽  
◽  
A.N. Nazarov ◽  
V.S. Lysenko ◽  
◽  
...  
Keyword(s):  
Silicon On Insulator ◽  
Basic Properties ◽  
Soi Devices

Basic Properties of an Ultrasonic Probe with a Through Hole for Puncture and Detection Principle of a Puncture Needle

2012 ◽  
Vol 132 (11) ◽  
pp. 420-424 ◽  
Author(s):  
Yuusuke Tanaka ◽  
Katsuhiko Tanaka ◽  
Susumu Sugiyama ◽  
Hisanori Shiomi ◽  
Yoshimasa Kurumi ◽  
...  
Keyword(s):  
Ultrasonic Probe ◽  
Basic Properties ◽  
Puncture Needle ◽  
Through Hole ◽  
Detection Principle

Continuity of homotopies

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Open Subset ◽  
Small Neighborhood ◽  
Unit Vector ◽  
Zariski Topology ◽  
Simple Point ◽  
Smooth Variety ◽  
Additional Material ◽  
Generic Type ◽  
Zariski Open Subset

This chapter includes some additional material on homotopies. In particular, for a smooth variety V, there exists an “inflation” homotopy, taking a simple point to the generic type of a small neighborhood of that point. This homotopy has an image that is properly a subset of unit vector V, and cannot be understood directly in terms of definable subsets of V. The image of this homotopy retraction has the merit of being contained in unit vector U for any dense Zariski open subset U of V. The chapter also proves the continuity of functions and homotopies using continuity criteria and constructs inflation homotopies before proving GAGA type results for connectedness. Additional results regarding the Zariski topology are given.

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.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

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