Bounded sets in fast complete inductive limits

Jan Kucera and Carlos Bosch

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-3

Abstract:

Let E 1 ⊂ E 2 ⊂ … be a sequence of locally convex spaces with all identity maps: E n → E n + 1 continuous and E = indlim E n fast complete. Then each set bounded in E is also bounded in some E n iff for any Banach disk B bounded in E and n ∈ N , the closure of B ⋂ E n in B is bounded in some E m . This holds, in particular, if all spaces E n are webbed.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:759768

DOI: 10.1155/S016117128400065X

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