Abstract
Every topological vector space E carries a natural uniform structure (in the sense of N. Bourbaki [2], see also H.Schubert [1]) which is determined by all sets {(x,y) ϵ E × E|x — y ϵ U}, U running through any 0-basis in E. Consequently, topological vector spaces are open for application of the results of the general theory of uniform spaces.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1981 B. G. Teubner, Stuttgart
About this chapter
Cite this chapter
Jarchow, H. (1981). Completeness. In: Locally Convex Spaces. Mathematische Leitfäden. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-90559-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-322-90559-8_3
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-90561-1
Online ISBN: 978-3-322-90559-8
eBook Packages: Springer Book Archive