Abstract
The topics of this chapter draw their motivation, with a locally convex space E, from two questions: find topologies on E″ such that the canonical mapping κ: E → E″ is continuous, and investigate properties of topologies on E ensuring that κ is continuous, if E″ is provided with the strong topology β(E″, E′). The first issue leads to the ‘natural topology’ on E″, the second leads to ‘quasi-barrelled’ spaces, and in particular, the answer to the second question motivates the investigation of further related properties of locally convex 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 subscriptionsReferences
G. Köthe: Topologische Lineare Räume I. 2nd edition. Springer, Berlin, 1966.
G. W. Mackey: On convex topological linear spaces. Trans. Amer. Math. Soc. 60, 519–537 (1946).
H. H. Schaefer: Topological Vector Spaces. 3rd edition. Springer, New York, 1971.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Voigt, J. (2020). Topologies on E″, Quasi-barrelled and Barrelled Spaces. In: A Course on Topological Vector Spaces. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-32945-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-32945-7_6
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-32944-0
Online ISBN: 978-3-030-32945-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)