Fundamentals of General Topology
| Author | : A.V. Arkhangel'skii |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 440 |
| Release | : 2001-11-30 |
| Genre | : Mathematics |
| ISBN | : 9781402003080 |
General Topology And Applications
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Topology with Applications
| Author | : Somashekhar A. Naimpally |
| Publisher | : World Scientific |
| Total Pages | : 294 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 9814407666 |
The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.
TOPO 72 - General Topology and its Applications
| Author | : R.A. Alo |
| Publisher | : Springer |
| Total Pages | : 669 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540383239 |
Sponsored by Carnegie-Mellon University and the University of Pittsburgh
General Topology
| Author | : Tom Richmond |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 370 |
| Release | : 2020-07-06 |
| Genre | : Mathematics |
| ISBN | : 3110686724 |
The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications. The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.
Recent Progress in General Topology II
| Author | : M. Husek |
| Publisher | : Elsevier |
| Total Pages | : 652 |
| Release | : 2002-11-13 |
| Genre | : Mathematics |
| ISBN | : 0444509801 |
The book presents surveys describing recent developments in most of the primary subfields of General Topology and its applications to Algebra and Analysis during the last decade. It follows freely the previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared in connection with the Prague Topological Symposium, held in 2001. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs slightly from those chosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including Infinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as: R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.
General Topology
| Author | : John L. Kelley |
| Publisher | : Courier Dover Publications |
| Total Pages | : 321 |
| Release | : 2017-03-07 |
| Genre | : Mathematics |
| ISBN | : 0486820661 |
Comprehensive text for beginning graduate-level students and professionals. "The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure." — Bulletin of the American Mathematical Society. 1955 edition.
Open Problems in Topology
| Author | : J. van Mill |
| Publisher | : North Holland |
| Total Pages | : 716 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : |
From the Introduction: This volume grew from a discussion by the editors on the difficulty of finding good thesis problems for graduate students in topology. Although at any given time we each had our own favorite problems, we acknowledged the need to offer students a wider selection from which to choose a topic peculiar to their interests. One of us remarked, 'Wouldn't it be nice to have a book of current unsolved problems always available to pull down from the shelf?' The other replied 'Why don't we simply produce such a book?' Two years later and not so simply, here is the resulting volume. The intent is to provide not only a source book for thesis-level problems but also a challenge to the best researchers in the field.
Topology and Robotics
| Author | : Michael Farber |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 202 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821842463 |
Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.
Recent Progress in General Topology III
| Author | : K.P. Hart |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 898 |
| Release | : 2013-12-11 |
| Genre | : Mathematics |
| ISBN | : 946239024X |
The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.
Applications of Algebraic Topology
| Author | : S. Lefschetz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 190 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468493671 |
This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.
