�ber einen Graphensatz f�r Abbildungen mit normiertem Zielraum

Eberhardt, Volker

doi:10.1007/bf01166233

Cited by 6 publications

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“…Theorem 8 and ( [4], l.k) show that the GM-property is an example of a property which is always inherited by countable codimensional vector subspaces but is never preserved by countable dimensional enlargements of the dual. Eberhardt's GiV-spaces [ 3 ] , which are also barrelled, exhibit rather different behaviour.…”

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confidence: 99%

On the stability of barrelled topologies, III

Robertson

Tweddle

Yeomans

1980

Bull. Austral. Math. Soc.

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Let E be a barrelled space with dual F # E* . It is shown that F has uncountable codimension in E* . If M is a vector subspace of E* of countable dimension with M n F = {o} , the topology x(E, F+M) is called a countable enlargement of f{E, F) . The results of the two previous papers are extended: it is proved that a non-barrelled countable enlargement always exists, and sufficient conditions for the existence of a barrelled countable enlargement are established, to include cases where the bounded sets may all be finite dimensional. An example of this case is given, derived from Amemiya and Komura; some specific and general classes of spaces containing a dense barrelled vector subspace of codimension greater than or equal to a are discussed. Completeness, codimension in E* and non-barrelled countable enlargementsWe use the notation and terminology of [7]

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confidence: 99%