Fundamentals Of General Topology
Download Fundamentals Of General Topology full books in PDF, epub, and Kindle. Read online free Fundamentals Of General Topology ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : William J. Pervin |
Publisher | : Academic Press |
Total Pages | : 222 |
Release | : 2014-05-12 |
Genre | : Mathematics |
ISBN | : 1483225151 |
Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction. This book provides a careful treatment of general topology. Organized into 11 chapters, this book begins with an overview of the important notions about cardinal and ordinal numbers. This text then presents the fundamentals of general topology in logical order processing from the most general case of a topological space to the restrictive case of a complete metric space. Other chapters consider a general method for completing a metric space that is applicable to the rationals and present the sufficient conditions for metrizability. This book discusses as well the study of spaces of real-valued continuous functions. The final chapter deals with uniform continuity of functions, which involves finding a distance that satisfies certain requirements for all points of the space simultaneously. This book is a valuable resource for students and research workers.
Author | : A.V. Arkhangel'skii |
Publisher | : Springer Science & Business Media |
Total Pages | : 440 |
Release | : 2001-11-30 |
Genre | : Mathematics |
ISBN | : 9781402003080 |
Author | : A.V. Arkhangel'skii |
Publisher | : Springer Science & Business Media |
Total Pages | : 210 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642612652 |
This is the first of the encyclopaedia volumes devoted to general topology. It has two parts. The first outlines the basic concepts and constructions of general topology, including several topics which have not previously been covered in English language texts. The second part presents a survey of dimension theory, from the very beginnings to the most important recent developments. The principal ideas and methods are treated in detail, and the main results are provided with sketches of proofs. The authors have suceeded admirably in the difficult task of writing a book which will not only be accessible to the general scientist and the undergraduate, but will also appeal to the professional mathematician. The authors' efforts to detail the relationship between more specialized topics and the central themes of topology give the book a broad scholarly appeal which far transcends narrow disciplinary lines.
Author | : Aleksandr Vladimirovič Arhangel'skij |
Publisher | : |
Total Pages | : 0 |
Release | : 1984 |
Genre | : |
ISBN | : |
Author | : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov |
Publisher | : American Mathematical Soc. |
Total Pages | : 432 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821886250 |
This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.
Author | : A. Arkhangelsky |
Publisher | : |
Total Pages | : |
Release | : 1979 |
Genre | : |
ISBN | : 9780720404951 |
Author | : K. D. Joshi |
Publisher | : New Age International |
Total Pages | : 430 |
Release | : 1983 |
Genre | : Topology |
ISBN | : 9780852264447 |
Author | : Avishek Adhikari |
Publisher | : Springer Nature |
Total Pages | : 523 |
Release | : 2022-07-04 |
Genre | : Mathematics |
ISBN | : 9811665095 |
This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone–Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the concepts leading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.
Author | : Tai-Danae Bradley |
Publisher | : MIT Press |
Total Pages | : 167 |
Release | : 2020-08-18 |
Genre | : Mathematics |
ISBN | : 0262359626 |
A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
Author | : George L. Cain |
Publisher | : Addison Wesley |
Total Pages | : 232 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : |
This introduction to point-set topology contains material on hyperspaces, malfunctions and dimension - topics important in the study of fractal geometry and chaotic dynamics. The book also includes examples, topics and applications. It aims to motivate students to think abstractly.