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Quasi-bounded sets

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  • Jan Kucera

Abstract

It is proved in [1] & [2] that a set bounded in an inductive limit E = indlim E n of Fréchet spaces is also bounded in some E n iff E is fast complete. In the case of arbitrary locally convex spaces E n every bounded set in a fast complete indlim E n is quasi-bounded in some E n , though it may not be bounded or even contained in any E n . Every bounded set is quasi-bounded. In a Fréchet space every quasi-bounded set is also bounded.

Suggested Citation

  • Jan Kucera, 1990. "Quasi-bounded sets," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 13, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:120153
    DOI: 10.1155/S0161171290000849
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