Abstract
Let E be a normed vector space (over the real or the complex numbers). We can define the notion of Cauchy sequence in E as we did for real sequences, and also the notion of convergent sequence (having a limit). If every Cauchy sequence converges, then E is said to be complete, and is also called a Banach space. A closed subspace of a Banach space is complete, hence it is also a Banach space.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lang, S. (1993). Continuous Functions on Compact Sets. In: Real and Functional Analysis. Graduate Texts in Mathematics, vol 142. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0897-6_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0897-6_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6938-0
Online ISBN: 978-1-4612-0897-6
eBook Packages: Springer Book Archive