On cm-bounding sets

Peter Biström; Sten Bjon; Mikael Lindström

doi:10.1017/S1446788700036946

On c^m-bounding sets

Peter Biström
, Sten Bjon
, Mikael Lindström

Matematik

Forskningsoutput: Tidskriftsbidrag › Artikel › Vetenskaplig › Peer review

1 Citeringar (Scopus)

Sammanfattning

Let E be a quasi-complete locally convex space and A a subset of E. It is shown that if every real-valued C^∞ -function in the weak topology of E is bounded on A, then A is relatively weakly compact. Furthermore, if all real-valued C^∞-functions on E are bounded on A, then A is relatively compact in the associated semi-weak topology of E.

Originalspråk	Engelska
Sidor (från-till)	20-28
Antal sidor	9
Tidskrift	Journal of the Australian Mathematical Society
Volym	54
Nummer	1
DOI	https://doi.org/10.1017/S1446788700036946
Status	Publicerad - feb. 1993
MoE-publikationstyp	A1 Tidskriftsartikel-refererad

Åtkomst av dokument

10.1017/S1446788700036946Licens: Ospecificerad

Andra filer och länkar

Länk till publikationen i Scopus

Citera det här

@article{55c48a37af3048c9aabeb2f805457d54,

title = "On cm-bounding sets",

abstract = "Let E be a quasi-complete locally convex space and A a subset of E. It is shown that if every real-valued C∞ -function in the weak topology of E is bounded on A, then A is relatively weakly compact. Furthermore, if all real-valued C∞-functions on E are bounded on A, then A is relatively compact in the associated semi-weak topology of E.",

keywords = "changeable double limit property, Cmbounding set, inter-, relatively compact set, semi-weak topology",

author = "Peter Bistr{\"o}m and Sten Bjon and Mikael Lindstr{\"o}m",

year = "1993",

month = feb,

doi = "10.1017/S1446788700036946",

language = "English",

volume = "54",

pages = "20--28",

journal = "Journal of the Australian Mathematical Society",

issn = "1446-7887",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - On cm-bounding sets

AU - Biström, Peter

AU - Bjon, Sten

AU - Lindström, Mikael

PY - 1993/2

Y1 - 1993/2

N2 - Let E be a quasi-complete locally convex space and A a subset of E. It is shown that if every real-valued C∞ -function in the weak topology of E is bounded on A, then A is relatively weakly compact. Furthermore, if all real-valued C∞-functions on E are bounded on A, then A is relatively compact in the associated semi-weak topology of E.

AB - Let E be a quasi-complete locally convex space and A a subset of E. It is shown that if every real-valued C∞ -function in the weak topology of E is bounded on A, then A is relatively weakly compact. Furthermore, if all real-valued C∞-functions on E are bounded on A, then A is relatively compact in the associated semi-weak topology of E.

KW - changeable double limit property

KW - Cmbounding set

KW - inter-

KW - relatively compact set

KW - semi-weak topology

UR - https://www.scopus.com/pages/publications/84972375616

U2 - 10.1017/S1446788700036946

DO - 10.1017/S1446788700036946

M3 - Article

AN - SCOPUS:84972375616

SN - 1446-7887

VL - 54

SP - 20

EP - 28

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 1