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

Matematiikka

Tutkimustuotos: Lehtiartikkeli › Artikkeli › Tieteellinen › vertaisarvioitu

1 Sitaatiot (Scopus)

Abstrakti

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.

Alkuperäiskieli	Englanti
Sivut	20-28
Sivumäärä	9
Julkaisu	Journal of the Australian Mathematical Society
Vuosikerta	54
Numero	1
DOI - pysyväislinkit	https://doi.org/10.1017/S1446788700036946
Tila	Julkaistu - helmik. 1993
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

Pääsy asiakirjaan

10.1017/S1446788700036946Lisenssi: Määrittelemätön

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Viittausmuodot

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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

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