Universal Spaces and Mappings PDF Download

Author: S.D. Iliadis
Publisher: Elsevier
ISBN: 0080457304
Category : Mathematics
Languages : en
Pages : 576

View

Book Description
Universal Spaces and Mappings is devoted to universality problems. A new approach to these problems is given using some specific spaces. Since the construction of these specific spaces is set-theoretical, the given theory can be applied to different topics of Topology such as: universal mappings, dimension theory, action of groups, inverse spectra, isometrical embeddings, and so on. Universal spaces Universal mappings Dimension theory Actions of groups Isometric Universal Spaces

Author: Stephen Lipscomb
Publisher: Springer Science & Business Media
ISBN: 0387854940
Category : Mathematics
Languages : en
Pages : 259

View

Book Description
Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric). The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval. Unique features include: * The use of graphics to illustrate the fractal view of these spaces; * Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology; * A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings; * Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study - the interested reader will find many relevant open problems which will create further research into these topics.

Author: Leon Armenovich Takhtadzhi︠a︡n
Publisher: American Mathematical Soc.
ISBN: 0821839365
Category : Mathematics
Languages : en
Pages : 136

View

Book Description
In this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).

Author: O. Lehto
Publisher: Springer Science & Business Media
ISBN: 1461386527
Category : Mathematics
Languages : en
Pages : 271

View

Book Description
This monograph grew out of the notes relating to the lecture courses that I gave at the University of Helsinki from 1977 to 1979, at the Eidgenossische Technische Hochschule Zurich in 1980, and at the University of Minnesota in 1982. The book presumably would never have been written without Fred Gehring's continuous encouragement. Thanks to the arrangements made by Edgar Reich and David Storvick, I was able to spend the fall term of 1982 in Minneapolis and do a good part of the writing there. Back in Finland, other commitments delayed the completion of the text. At the final stages of preparing the manuscript, I was assisted first by Mika Seppala and then by Jouni Luukkainen, who both had a grant from the Academy of Finland. I am greatly indebted to them for the improvements they made in the text. I also received valuable advice and criticism from Kari Astala, Richard Fehlmann, Barbara Flinn, Fred Gehring, Pentti Jarvi, Irwin Kra, Matti Lehtinen, I1ppo Louhivaara, Bruce Palka, Kurt Strebel, Kalevi Suominen, Pekka Tukia and Kalle Virtanen. To all of them I would like to express my gratitude. Raili Pauninsalo deserves special thanks for her patience and great care in typing the manuscript. Finally, I thank the editors for accepting my text in Springer-Verlag's well known series. Helsinki, Finland June 1986 Olli Lehto Contents Preface. ... v Introduction ...

Author: Arnold Koslow
Publisher: Springer
ISBN: 3319101935
Category : Mathematics
Languages : en
Pages : 519

View

Book Description
This is the first volume of a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of topics including combination of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic (Aristotle, Avicenna, Buridan, Schröder, MacColl). This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic.

Author: D. Repovs
Publisher: Springer Science & Business Media
ISBN: 9401711623
Category : Mathematics
Languages : en
Pages : 366

View

Book Description
This book is dedicated to the theory of continuous selections of multi valued mappings, a classical area of mathematics (as far as the formulation of its fundamental problems and methods of solutions are concerned) as well as !'J-n area which has been intensively developing in recent decades and has found various applications in general topology, theory of absolute retracts and infinite-dimensional manifolds, geometric topology, fixed-point theory, functional and convex analysis, game theory, mathematical economics, and other branches of modern mathematics. The fundamental results in this the ory were laid down in the mid 1950's by E. Michael. The book consists of (relatively independent) three parts - Part A: Theory, Part B: Results, and Part C: Applications. (We shall refer to these parts simply by their names). The target audience for the first part are students of mathematics (in their senior year or in their first year of graduate school) who wish to get familiar with the foundations of this theory. The goal of the second part is to give a comprehensive survey of the existing results on continuous selections of multivalued mappings. It is intended for specialists in this area as well as for those who have mastered the material of the first part of the book. In the third part we present important examples of applications of continuous selections. We have chosen examples which are sufficiently interesting and have played in some sense key role in the corresponding areas of mathematics.

Author: Ward, Lock and co, ltd
Publisher:
ISBN:
Category :
Languages : en
Pages : 968

View

Book Description

Author: K.P. Hart
Publisher: Elsevier
ISBN: 0080530869
Category : Mathematics
Languages : en
Pages : 537

View

Book Description
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.Key features:• More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms

Author: Pol Bargués-Pedreny
Publisher: Routledge
ISBN: 1351124463
Category : Political Science
Languages : en
Pages : 427

View

Book Description
Throughout history, maps have been a powerful tool in the constitutive imaginary of governments seeking to define or contest the limits of their political reach. Today, new digital technologies have become central to mapping as a way of formulating alternative political visions. Mapping can also help marginalised communities to construct speculative designs using participatory practices. Mapping and Politics in the Digital Age explores how the development of new digital technologies and mapping practices are transforming global politics, power, and cooperation. The book brings together authors from across political and social theory, geography, media studies and anthropology to explore mapping and politics across three sections. Contestations introduces the reader to contemporary developments within mapping and explores the politics of mapping as a form of knowledge and contestation. Governance analyses mapping as a set of institutional practices, providing key methodological frames for understanding global governance in the realms of urban politics, refugee control, health crises and humanitarian interventions and new techniques of biometric regulation and autonomic computation. Imaginaries provides examples of future-oriented analytical frameworks, highlighting the transformation of mapping in an age of digital technologies of control and regulation. In a world conceived as without borders and fixed relations, new forms of mapping stress the need to rethink assumptions of power and knowledge. This book provides a sophisticated and nuanced analysis of the role ofmapping in contemporary global governance, and will be of interest to students and researchers working within politics, geography, sociology, media, and digital culture and technology.

Author: Podobnikar, Tomaž
Publisher: IGI Global
ISBN: 1466603283
Category : Technology & Engineering
Languages : en
Pages : 305

View

Book Description
A universal approach to the ontology of geographic space has already been, and is going to be, a comprehensive task for establishing more effective spatial models. The concept of a universal spatial ontology should be independent of location, culture, and time. It should be fundamental and universal in the same way that the number p defines the ratio between the diameter and the circumference of a circle. The term “universal” therefore means all-embracing and for general propose. Universal Ontology of Geographic Space: Semantic Enrichment for Spatial Data aims to escalate the current scope of research to support the development of semantically interoperable systems of geographic space. This reference will aid university lecturers and professors, students, researchers, developers of spatial applications.