## Barrelledness in topological and ordered vector spaces |

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### Contents

CHAPTER | 1 |

Locally convex spaces | 8 |

The HahnBanach theorem | 10 |

Copyright | |

30 other sections not shown

### Common terms and phrases

a-barrelled absorbing Banach Spaces Banach-Steinhaus theorem bornologica1 bornological space bounded set bounded subset C.O.Q. vector lattice Cauchy Chapter circled and convex Clearly closure coarser codimension completes the proof convex neighbourhood Corollary 12 countably barrelled space defining sequence Definition DF)-space dual pair Edited equicontinuous equicontinuous subset Example f e H f is continuous fundamental sequence H is equicontinuous H-space Hausdorff hence a neighbourhood implies inductive limit isomorphism lattice ideal Lemma Let E,C,u Let E,u Let f linear functional linear topology locally convex Mackey topology metrizable 1.c metrizable t.v. space neighbourhood basis O.Q.U. vector lattice order-quasibarrelled vector lattice ordered 1.c ordered t.v. space ordered vector space pointwise bounded precompact Proceedings Proposition relative topology Schauder basis seminorm sequentially complete space and F space is barrelled statements are equivalent t.v. lattice topological vector spaces ultrabarrelled space ultrabornological Vlll