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 |
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Pages (from-to) | 20-28 |
Number of pages | 9 |
Journal | Journal of the Australian Mathematical Society |
Volume | 54 |
Issue number | 1 |
DOIs | |
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