Bộ sách luyện thi ETS 2023 LC&RC
199,000₫
299,000₫
Sách Basic Topology 1,2,3 (sách keo gáy, bìa mềm)
Thể loại:Mathematics - Geometry and Topology
Năm:2022
In lần thứ:1
Ngôn ngữ:english
Main subject categories: • Topology • Topological linear spaces and
related structures • Spaces determined by compactness or summability
properties • Normed linear spaces and Banach spaces; Banach lattices
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.
