Topological Vector Spaces

Taqdir Husain
Additional contact information
Taqdir Husain: McMaster University

Chapter 2 in The Open Mapping and Closed Graph Theorems in Topological Vector Spaces, 1965, pp 11-33 from Springer

Abstract: Abstract Definition 1. (a) A set E u is said to be a topological vector space (or, in short, a TVS) over a given field K, if E u as a pointset is a topological space and a vector space over K such that the mappings: % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaGGOa % GaamiEaiaacYcacaWG5bGaaiykaiabgkziUkaadIhacqGHRaWkcaWG % 5bGaaiilaaqaaiaacIcacqaH7oaBcaGGSaGaamiEaiaacMcacqGHsg % IRcqaH7oaBcaWG4baaaaa!48D1! $$\begin{gathered} (x,y) \to x + y, \hfill \\ (\lambda ,x) \to \lambda x \hfill \\ \end{gathered}$$ are continuous in both variables together for x, y ∈ E and λ ∈ K.

Keywords: Convex Hull; Topological Vector Space; Finite Subset; Inductive Limit; Fundamental System (search for similar items in EconPapers)
Date: 1965
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:978-3-322-96210-2_2

Ordering information: This item can be ordered from
http://www.springer.com/9783322962102

DOI: 10.1007/978-3-322-96210-2_2

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 ().