## Barrelledness in topological and ordered vector spaces |

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### Contents

Topological vector spaces | 1 |

Locally convex spaces | 8 |

The HahnBanach theorem | 10 |

Copyright | |

32 other sections not shown

### Other editions - View all

Barrelledness in Topological and Ordered Vector Spaces T. Husain,S.M. Khaleelulla Limited preview - 2006 |

### Common terms and phrases

a-barrelled absorbing Banach barrelled space bornological space bounded sets bounded subset C.O.Q. vector lattice called Chapter circled and convex circled convex Clearly closure codimension completes the proof cone continuous linear map converges convex neighbourhood Corollary l0 countably barrelled space countably quasibarrelled countably ultrabarrelled Definition DF)-space dual pair equicontinuous equicontinuous subset f is continuous H is equicontinuous H-space Hausdorff hence a neighbourhood I.c. space I.c. space E,u I.c. vector lattice implies inductive limit isomorphism Lemma Let E,C,u Let E,u Let f linear topology locally convex spaces metrizable I.c. space neighbourhood basis O.Q.U. vector lattice order-bornivorous order-quasibarrelled vector lattice ordered I.c. ordered t.v. space ordered vector space pointwise bounded precompact Proposition quasibarrelled space relative topology Schauder basis seminorm sequentially complete space and F,v space is barrelled statements are equivalent t.v. lattice Theorem topological vector spaces ultrabarrelled space