Brief History of Topological Groups, Manifolds and Lie Groups

Avishek Adhikari () and Mahima Ranjan Adhikari
Additional contact information
Avishek Adhikari: Presidency University, Department of Mathematics
Mahima Ranjan Adhikari: Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC)

Chapter Chapter 5 in Basic Topology 2, 2022, pp 355-364 from Springer

Abstract: Abstract This chapter conveys the history of emergence of the concepts leading to the development of topological groups, manifolds and also Lie groups as mathematical topics with their motivations with their motivations. They are specialized topological spaces having additional structures other than the topological structures which are interlinked. Historically, the word “topology” comes from the Greek words $$ ``\lambda $$ ` ` λ ó $$\gamma o\zeta $$ γ o ζ ” and $$``\tau $$ ` ` τ ó $$\pi $$ π o $$\varsigma $$ ς ” with an alternative name “analysis situs” aiming at the study of situations. This subject arising as a branch of geometry plays a key role in modern mathematics, because of its study of continuous deformations such as stretching, twisting, crumpling and bending, which are allowed, whereas tearing or gluing are not allowed.

Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-16-6577-6_5

Ordering information: This item can be ordered from
http://www.springer.com/9789811665776

DOI: 10.1007/978-981-16-6577-6_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().