Topological Groups and Related Structures, An Introduction to Topological Algebra.
Synopsis
Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.Book details
- Edition:
- 2008
- Series:
- Atlantis Studies in Mathematics (Book 1)
- Author:
- Alexander Arhangel’skii, Mikhail Tkachenko
- ISBN:
- 9789491216350
- Publisher:
- Atlantis Press, Paris
- Pages:
- N/A
- Reading age:
- Not specified
- Includes images:
- No
- Date of addition:
- 2022-08-15
- Usage restrictions:
- Copyright
- Copyright date:
- 2008
- Copyright by:
- N/A
- Adult content:
- No
- Language:
- English
- Categories:
- Mathematics and Statistics, Nonfiction