Basic Concepts of Manifolds

Amiya Mukherjee
Additional contact information
Amiya Mukherjee: Indian Statistical Institute, Statistics and Mathematics Unit

Chapter Chapter 1 in Differential Topology, 2015, pp 1-42 from Springer

Abstract: Abstract There are two ways one can look at a differentiable manifold. Firstly, it is a topological space with a structure which helps us to define differentiable functions on it, just as a topological structure on a set is designed to define continuous functions on that set. Secondly, it is a topological space which can be obtained by gluing together open subsets of some Euclidean space in a nice way; think, for example, of the surface of a ball or a torus covered with small paper disks pasted together on overlaps without making any crease or fold.

Keywords: Open Subset; Open Neighbourhood; Smooth Manifold; Local Representation; Grassmann Manifold (search for similar items in EconPapers)
Date: 2015
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:978-3-319-19045-7_1

Ordering information: This item can be ordered from
http://www.springer.com/9783319190457

DOI: 10.1007/978-3-319-19045-7_1

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 ().