Quasi-bounded sets

Jan Kucera

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-4

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.

Date: 1990
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DOI: 10.1155/S0161171290000849

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