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Books in Algebraic topology

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Handbook of Truly Concurrent Process Algebra

  • 1st Edition
  • December 1, 2023
  • Yong Wang
  • English
  • Paperback
    9 7 8 - 0 - 4 4 3 - 2 1 5 1 5 - 5
  • eBook
    9 7 8 - 0 - 4 4 3 - 2 1 5 1 6 - 2
Handbook of Truly Concurrent Process Algebra provides readers with a detailed and in-depth explanation of the algebra used for concurrent computing. This complete handbook is divided into five Parts: Algebraic Theory for Reversible Computing, Probabilistic Process Algebra for True Concurrency, Actors – A Process Algebra-Based Approach, Secure Process Algebra, and Verification of Patterns. The author demonstrates actor models which are captured using the following characteristics: Concurrency, Asynchrony, Uniqueness, Concentration, Communication Dependency, Abstraction, and Persistence. Every pattern is detailed according to a regular format to be understood and utilized easily, which includes introduction to a pattern and its verifications.Patterns of the vertical domains are also provided, including the domains of networked objects and resource management. To help readers develop and implement the software patterns scientifically, the pattern languages are also presented.

Projective Transformations

  • 1st Edition
  • May 12, 2014
  • P. S. Modenov + 1 more
  • Henry Booker + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 6 1 4 9 - 2
Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserving transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

Algebraic and Classical Topology

  • 1st Edition
  • May 9, 2014
  • I. M. James
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 8 4 7 7 - 7
Algebraic and Classical Topology contains all the published mathematical work of J. H. C. Whitehead, written between 1952 and 1960. This volume is composed of 21 chapters, which represent two groups of papers. The first group, written between 1952 and 1957, is principally concerned with fiber spaces and the Spanier-Whitehead S-theory. In the second group, written between 1957 and 1960, Whitehead returns to classical topology after a long interval, and participates in the renewed assault on the problems which fascinated him most. This book will prove useful to mathematicians.

Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures and Applications

  • 1st Edition
  • Volume 199
  • January 20, 2005
  • Badri Dvalishvili
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 4 5 9 4 6 - 2
This monograph is the first and an initial introduction to the theory of bitopological spaces and its applications. In particular, different families of subsets of bitopological spaces are introduced and various relations between two topologies are analyzed on one and the same set; the theory of dimension of bitopological spaces and the theory of Baire bitopological spaces are constructed, and various classes of mappings of bitopological spaces are studied. The previously known results as well the results obtained in this monograph are applied in analysis, potential theory, general topology, and theory of ordered topological spaces. Moreover, a high level of modern knowledge of bitopological spaces theory has made it possible to introduce and study algebra of new type, the corresponding representation of which brings one to the special class of bitopological spaces. It is beyond any doubt that in the nearest future the areas of essential applications will be the theories of linear topological spaces and topological groups, algebraic and differential topologies, the homotopy theory, not to mention other fundamental areas of modern mathematics such as geometry, mathematical logic, the probability theory and many other areas, including those of applied nature. Key Features:- First monograph is "Generalized Lattices"

Topological Algebras

  • 1st Edition
  • Volume 185
  • November 23, 2000
  • V.K. Balachandran
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 4 3 0 8 - 6
This book consists of nine chapters. Chapter 1 is devoted to algebraic preliminaries. Chapter 2 deals with some of the basic definition and results concerning topological groups, topological linear spaces and topological algebras. Chapter 3 considered some generalizations of the norm. Chapter 4 is concerned with a generalization of the notion of convexity called p-convexity. In Chapter 5 some differential and integral analysis involving vector valued functions is developed. Chapter 6 is concerned with spectral analysis and applications. The Gelfand representation theory is the subject-matter of Chapter 7. Chapter 8 deals with commutative topological algebras. Finally in Chapter 9 an exposition of the norm uniqueness theorems of Gelfand and Johnson (extended to p-Banach algebras) is given.

The Mathematical Theory of Knots and Braids

  • 1st Edition
  • Volume 82
  • April 1, 2000
  • S. Moran
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 1 9 3 - 6
This book is an introduction to the theory of knots via the theory of braids, which attempts to be complete in a number of ways. Some knowledge of Topology is assumed. Necessary Group Theory and further necessary Topology are given in the book. The exposition is intended to enable an interested reader to learn the basics of the subject. Emphasis is placed on covering the theory in an algebraic way. The work includes quite a number of worked examples. The latter part of the book is devoted to previously unpublished material.

History of Topology

  • 1st Edition
  • August 24, 1999
  • I.M. James
  • English
  • Hardback
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  • eBook
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Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

Handbook of Algebraic Topology

  • 1st Edition
  • July 18, 1995
  • I.M. James
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 3 2 9 8 - 1
Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.

Differential Topology

  • 1st Edition
  • Volume 173
  • June 2, 1992
  • J. Margalef-Roig + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 8 4 - 1
...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry.Peter W. Michor

Lectures on Homotopy Theory

  • 1st Edition
  • Volume 171
  • January 21, 1992
  • R.A. Piccinini
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 8 2 - 7
The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps.Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity.