压缩
发表于 2025-3-21 18:19:21
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euphoria
发表于 2025-3-21 22:25:29
Uniform convergence spaces,e convergence generalization of uniform spaces, are not as strong as their topological counterparts. In particular uniform continuity is not a very strong property. But basically all properties of completeness can be carried over to uniform convergence spaces and equicontinuity is an even stronger c
华而不实
发表于 2025-3-22 01:14:49
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LAIR
发表于 2025-3-22 05:49:53
Hahn-Banach extension theorems,or subspace of . with the property that . ∩.. is closed in each .. - such a subspace is called stepwise closed. Further, let φ bea sequentially continuous linear functional on .. Does there exist a (sequentially) continuous linear extension to .? This is a difficult and much researched problem. Subs
暗语
发表于 2025-3-22 12:29:36
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incontinence
发表于 2025-3-22 14:20:32
The Banach-Steinhaus theorem,are locally convex topological vector spaces and . is barrelled, then every pointwise bounded subset of ?. is equicontinuous. This powerful theorem is used, for example to show that the pointwise limit of a sequence of continuous linear mappings is a continuous linear mapping. It is used as well to
incontinence
发表于 2025-3-22 19:09:47
Duality theory for convergence groups,ter group, i.e., the character group of its character group. Here each character group carries the compact-open topology. There are various generalizations of this result to not necessarily locally compact, commutative topological groups. Probably the first one was due to S. Kaplan who generalized t
Callus
发表于 2025-3-23 00:48:56
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Petechiae
发表于 2025-3-23 02:52:53
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使无效
发表于 2025-3-23 06:47:10
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