Inductive limits of topologies, their direct products, and problems related to algebraic structures
Inductive limits of topologies, their direct products, and problems related to algebraic structures
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拓扑的归纳极限、它们的直积以及与代数结构相关的问题
DOI：
10.1215/kjm/1250517614
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发表时间：
2001
影响因子：
--
通讯作者：
E. Hirai
中科院分区：
文献类型：
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作者：
T. Hirai;Hiroaki Shimomura;Nobuhiko Tatsuuma;E. Hirai
这篇论文是我们以前工作的延续。一半,我们研究了电感限制G = lim→Gn的拓扑组织Gn, n≥1,并证明了电感限制拓扑τ印第安纳= lim→τGn的拓扑τGn对Gn一般不给一组拓扑G,与肯定的声明(4,第210条),然后研究τ印第安纳州,我们构造,在温和条件下(PTA),一组拓扑τb = BS-lim→τGn G,称为笋拓扑,它是弱于或等于τ的粒子中最强的。这项工作给我们带来了两个研究方向。一是研究这种病理现象普遍发生的原因。二是在拓扑代数、拓扑半群等不同的范畴中构造归纳极限的良好版本（如拓扑群范畴中的τ BS）。
This paper is a continuation of our previous work [9]. In a half of it, we studied the inductive limit G = lim→Gn of topological groups Gn, n ≥ 1, and proved that the inductive limit topology τ ind = lim→ τGn of topologies τGn on Gn does not in general give a group topology on G, contrary to the affirmative statement in [4, Article 210], and then studying τ ind in detail, we constructed, under a mild condition (PTA), a group topology τ BS = BS-lim→ τGn on G, called Bamboo-Shoot topology, which is the strongest among those weaker than or equal to τ ind. This work provokes us two directions of study. The one is to study the reason why this kind of pathological phenomena occur rather in general. The other is to construct a good version of inductive limits (like τ BS in the category of topological groups) in various categories, such as topological algebras, topological semigroups etc.