A note on \(B\)-complete spaces and the closed graph theorem (Q1097461)
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scientific article; zbMATH DE number 4034379
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on \(B\)-complete spaces and the closed graph theorem |
scientific article; zbMATH DE number 4034379 |
Statements
A note on \(B\)-complete spaces and the closed graph theorem (English)
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1988
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It is proved that a generalized *-inductive limit \(E\) of a sequence of compact sets is \(B\)-complete, and that a closed linear map from \(E\) into itself is continuous, though this fails for an arbitrary \(B\)-complete space. It is also shown that a \(B\)-complete space in which subspaces are closed, has countable dimension.
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generalized *-inductive limit
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sequence of compact sets
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B-complete
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