Dense barrelled subspaces of uncountable codimension
| Autor: | Wendy J. Robertson, Stephen A. Saxon |
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| Rok vydání: | 1989 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 107:1021-1029 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-1989-0990433-2 |
| Popis: | Let E E be a Hausdorff barrelled space. If there exists a dense barrelled subspace M M such that ( codim ( M ) ≥ c ) [ codim ( M ) = dim ( E ) ] (\operatorname {codim} (M) \geq c)[\operatorname {codim} (M) = \operatorname {dim} (E)] , we say that ( M M is a satisfactory subspace [11]) [ E E is barrelledly fit], respectively. Robertson, Tweddle and Yeomans [11] proved that E E has a barrelled countable enlargement (BCE) if it has a satisfactory subspace. (Trivially) E E has a satisfactory subspace if dim ( E ) ≥ c \dim (E) \geq c and E E is barrelledly fit. We show that E E is barrelledly fit (and dim ( E ) ≥ c \dim (E) \geq c ) if E ≆ φ E \ncong \varphi and either (i) E E is an (LF)-space, or (ii) E E is an infinite-dimensional separable space and the continuum hypothesis holds. Conclusion: barrelledly fit spaces and their permanence properties arise from and advance the study of BCE’s. |
| Databáze: | OpenAIRE |
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