Topological Properties of Limits of Inverse Systems Of Measures

1974 ◽  
Vol 26 (6) ◽  
pp. 1455-1465 ◽  
Author(s):  
Donald J. Mallory
Keyword(s):  
Inverse Limit ◽  
Product Space ◽  
Point Of View ◽  
Limit Set ◽  
Topological Properties ◽  
Limit Measure ◽  
Radon Measures ◽  
Inverse Systems ◽  
Similar Point ◽  
Measure Spaces

It has been shown (Mallory and Sion [6]) that the problem of finding "limit" measures for inverse systems of measure spaces (Xi, μi)i∊I can be successfully attacked by establishing the existence of a “limit” measure on the product space , then considering the restriction to the inverse limit set .In this paper we use a similar point of view to establish conditions under which a system of Radón measures has a “limit” measure which is also Radón.

Profinite Modules

1973 ◽  
Vol 16 (3) ◽  
pp. 405-415
Author(s):  
Gerard Elie Cohen
Keyword(s):  
Finite Group ◽  
General Theory ◽  
Finite Length ◽  
Finite Groups ◽  
Inverse Limit ◽  
Abelian Groups ◽  
Point Of View ◽  
Inverse Limits ◽  
Profinite Groups ◽  
Inverse Systems

An inverse limit of finite groups has been called in the literature a pro-finite group and we have extensive studies of profinite groups from the cohomological point of view by J. P. Serre. The general theory of non-abelian modules has not yet been developed and therefore we consider a generalization of profinite abelian groups. We study inverse systems of discrete finite length R-modules. Profinite modules are inverse limits of discrete finite length R-modules with the inverse limit topology.

scholarly journals Real Tropicalization and Analytification of Semialgebraic Sets

2020 ◽  
Author(s):  
Philipp Jell ◽  
Claus Scheiderer ◽  
Josephine Yu
Keyword(s):  
Inverse Limit ◽  
Point Of View ◽  
General Point ◽  
Real Spectrum ◽  
Closed Field ◽  
Topological Properties ◽  
Absolute Value ◽  
The Real ◽  
Semialgebraic Set ◽  
Refined Version

Abstract Let $K$ be a real closed field with a nontrivial non-archimedean absolute value. We study a refined version of the tropicalization map, which we call real tropicalization map, that takes into account the signs on $K$. We study images of semialgebraic subsets of $K^n$ under this map from a general point of view. For a semialgebraic set $S \subseteq K^n$ we define a space $S_r^{{\operatorname{an}}}$ called the real analytification, which we show to be homeomorphic to the inverse limit of all real tropicalizations of $S$. We prove a real analogue of the tropical fundamental theorem and show that the tropicalization of any semialgebraic set is described by tropicalization of finitely many inequalities, which are valid on the semialgebraic set. We also study the topological properties of real analytification and tropicalization. If $X$ is an algebraic variety, we show that $X_r^{{\operatorname{an}}}$ can be canonically embedded into the real spectrum $X_r$ of $X$, and we study its relation with the Berkovich analytification of $X$.

scholarly journals Maintaining and Improving the Environmental Cleanliness in Semarang Municipality in the Era of Industrial Revolution 4.0

2019 ◽  
Vol 125 ◽  
pp. 04003
Author(s):  
Oktiva Herry Chandra
Keyword(s):  
Public Space ◽  
Industrial Revolution ◽  
Point Of View ◽  
Policy Makers ◽  
Form And Function ◽  
Similar Point ◽  
The Face ◽  
Observation Method ◽  
And Function ◽  
Participatory Observation

Language produced in a specific event of communication will have its form and function. Some messages are delivered in direct ways meaning the form and the functions are symmetric; some others are delivered in indirect ways, asymmetric. Direct or indirect ways will give different perceptions to those who receive the content of the message. Considering the face of receivers is one of the principles that should be made by policy makers as they communicate with people in public space. This article aims to explain the forms of language used to prohibit littering and the way the maker of prohibition thinks about the writing of littering. The research is conducted by using non-participatory observation method. This, then, is followed by applying note taking technique and recording. The result shows mostly the writings of littering prohibition are made an indirect way and less number in indirect way. Having a direct way means society is placed as subordinate in relation to the authorities. Even though less in number, indirect littering prohibition shows some writings see an equal position between the writer and reader. Both take a similar point of view on littering.

Concerning the First Course in Algebra

1952 ◽  
Vol 45 (1) ◽  
pp. 10-12
Author(s):  
Herbert Bernhardt
Keyword(s):  
Mathematics Teacher ◽  
Point Of View ◽  
Similar Point

In the April, 1950 issue of The Mathematics Teacher William R. Ransom1 suggests a more meaningful approach to the teaching of combination of like terms than that usually found in the first course in algebra. The present paper describes an attempt to apply a somewhat similar point of view to the entire beginning course in algebra.

TOPOLOGICAL PROPERTIES OF THE (n,k)-STAR GRAPH

1998 ◽  
Vol 09 (02) ◽  
pp. 235-248 ◽  
Author(s):  
WEI-KUO CHIANG ◽  
RONG-JAYE CHEN
Keyword(s):  
Average Distance ◽  
Point Of View ◽  
Attractive Alternative ◽  
Star Graph ◽  
Topological Properties ◽  
Major Drawback ◽  
Arrangement Graph ◽  
Different Types ◽  
Theory Point ◽  
Very High

The star graph, though an attractive alternative to the hypercube, has a major drawback in that the number of nodes for an n-star graph must be n!, and thus considerably limits the choice of the number of nodes in the graph. In order to alleviate this drawback, the arrangement graph was recently proposed as a generalization of the star graph topology. The arrangement graph provides more flexibility than the star graph in choosing the number of nodes, but the degree of the resulting network may be very high. To overcome that disadvantage, this paper presents another generalization of the star graph, called the (n,k)-star graph. We examine some topological properties of the (n,k)-star graph from the graph-theory point of view. It is shown that two different types of edges in the (n,k)-star prevent it from being edge-symmetric, but edges in each class are essentially symmetric with respect to each other. Also, the diameter and the exact average distance of the (n,k)-star graph are derived. In addition, the fault-diameter for the (n,k)-star graph is shown to be at most the fault-free diameter plus three.

scholarly journals Inverse Limit Spaces Satisfying a Poincaré Inequality

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Jeff Cheeger ◽  
Bruce Kleiner
Keyword(s):  
Banach Space ◽  
Large Class ◽  
Inverse Limit ◽  
Poincaré Inequality ◽  
Doubling Condition ◽  
Poincare Inequality ◽  
Inverse Limit Spaces ◽  
Inverse Systems ◽  
Nikodym Property

Abstract We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces, and a large class of new examples. As follows easily from [4], generically our examples have the property that they do not bilipschitz embed in any Banach space with Radon-Nikodym property. For Laakso spaces, thiswas noted in [4]. However according to [7] these spaces admit a bilipschitz embedding in L1. For Laakso spaces, this was announced in [5].

Assur’s Groups, AKCs, Basic Trusses, SOCs, etc.: Modular Kinematics of Planar Linkages

1996 ◽  
Author(s):  
E. Ceresole ◽  
P. Fanghella ◽  
C. Galletti
Keyword(s):  
Kinematic Chain ◽  
Point Of View ◽  
Robot Kinematics ◽  
Systems Of Equations ◽  
Topological Properties ◽  
Cad Systems ◽  
Solution Algorithms ◽  
Modular Method ◽  
The Common ◽  
Planar Linkages

Abstract The paper presents a unified point of view on modular methods of kinematic analysis of planar linkages. It is shown that various approaches adopted in different fields, such as linkage analysis, robot kinematics, variational CAD systems, are based on the common idea of decoupling complex systems of equations by solving sequences of simpler subsystems. These subsystems correspond to modules with particular topological properties. Then, the three main issues of a modular method, namely, systematic topology of the modules, solution algorithms for each module, and module recognition in a given mechanism, are discussed and solutions are provided by means of the general unifying concept of Assur Kinematic Chain (AKC).

scholarly journals Natural Theology, Philosophical Theology and Illustrative Argumentation

Open Theology ◽  
2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Vladimir K. Shokhin
Keyword(s):  
Natural Theology ◽  
Point Of View ◽  
Philosophical Theology ◽  
Strict Sense ◽  
History Of Thought ◽  
Religious Traditions ◽  
Rational Theology ◽  
Teleological Argument ◽  
Similar Point ◽  
History Of

AbstractI will attempt to define what we understand as “narrative argumentation” or “narrative arguments” through an appeal to a discussion of intercultural rational theology. In this context I offer a distinction between two concepts, which are considered usually as synonymous. Philosophical theology is regarded from the historical point of view as the whole repertoire of attempts at rational justification of the faith in God along with analysis of His attributes and actions within different religious traditions (both ancient and modern, Western and Eastern), whereas Natural Theology is regarded as a philosophical preparation for the theology of Revelation in traditional Christianity. Varieties of the teleological argument, which have been developed in the history of thought as the argument from analogy, i.e., from vivid examples aiming at persuasion of an opponent and audience in the dialectical controversy, are classified into two species of short-cut illustrative examples and the species of full-fledged theological parables, i.e., narratives in the strict sense. I conclude this discussion with an invitation to investigate other main theological arguments from a similar point of view.

scholarly journals Characterizing weak topological properties: Berry phase point of view

2014 ◽  
Vol 90 (15) ◽  
Author(s):  
Yukinori Yoshimura ◽  
Ken-Ichiro Imura ◽  
Takahiro Fukui ◽  
Yasuhiro Hatsugai
Keyword(s):  
Berry Phase ◽  
Point Of View ◽  
Phase Point ◽  
Topological Properties

scholarly journals SMOOTH METRIC MEASURE SPACES AND QUASI-EINSTEIN METRICS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250110 ◽  
Author(s):  
JEFFREY S. CASE
Keyword(s):  
Einstein Metrics ◽  
Conformal Geometry ◽  
Point Of View ◽  
Metric Measure Spaces ◽  
Unified Framework ◽  
Variational Characterization ◽  
Gradient Ricci Solitons ◽  
Smooth Metric Measure Spaces ◽  
Measure Spaces

Smooth metric measure spaces have been studied from the two different perspectives of Bakry–Émery and Chang–Gursky–Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Einstein metrics, conformally Einstein metrics, gradient Ricci solitons and static metrics. In this paper, we describe a natural perspective on smooth metric measure spaces from the point of view of conformal geometry and show how it unites these earlier perspectives within a unified framework. We offer many results and interpretations which illustrate the unifying nature of this perspective, including a natural variational characterization of quasi-Einstein metrics as well as some interesting families of examples of such metrics.

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