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

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

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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.

Original language	English
Pages (from-to)	20-28
Number of pages	9
Journal	Journal of the Australian Mathematical Society
Volume	54
Issue number	1
DOIs	https://doi.org/10.1017/S1446788700036946
Publication status	Published - Feb 1993
MoE publication type	A1 Journal article-refereed

Keywords

changeable double limit property
Cmbounding set
inter-
relatively compact set
semi-weak topology

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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.

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KW - Cmbounding set

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KW - semi-weak topology

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On c^m-bounding sets

Abstract

Keywords

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