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If not distinguished, is 𝐶_{𝑝}(𝑋) even close?
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-25 , DOI: 10.1090/proc/15439 J. C. Ferrando , Stephen A. Saxon
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-25 , DOI: 10.1090/proc/15439 J. C. Ferrando , Stephen A. Saxon
Abstract: is distinguished the strong dual is barrelled the strong bidual . So one may judge how nearly distinguished is by how nearly barrelled is, and also by how near the dense subspace is to the Baire space . Being Baire-like, is always fairly close to in that sense. But if is not distinguished, we show the codimension of is uncountable, i.e., is algebraically far from , and moreover, is very far from barrelled, not even primitive. Thus we profile weak barrelledness for and spaces. At the same time, we characterize those Tychonoff spaces for which is distinguished, solving the original problem from our series of papers.
中文翻译:
如果不区分,𝐶_{𝑝}(𝑋)甚至会关闭吗?
摘要:尊贵的双重对桶的坚强的双strong 。因此,可以判断出近乎有区别的有多近乎桶形,以及有致密的子空间离Baire空间有多近。从某种意义上说,像贝儿一样,总是很接近。但是,如果不加以区分,则表明的余维是不可数的,即,在代数上远离,而且与桶形相距甚远,甚至不是原始的。因此,我们分析了和空间的弱桶状度。与此同时,我们描述了那些吉洪诺夫空间为这 卓著,解决了我们系列论文中的原始问题。
更新日期:2021-04-22
中文翻译:
如果不区分,𝐶_{𝑝}(𝑋)甚至会关闭吗?
摘要:尊贵的双重对桶的坚强的双strong 。因此,可以判断出近乎有区别的有多近乎桶形,以及有致密的子空间离Baire空间有多近。从某种意义上说,像贝儿一样,总是很接近。但是,如果不加以区分,则表明的余维是不可数的,即,在代数上远离,而且与桶形相距甚远,甚至不是原始的。因此,我们分析了和空间的弱桶状度。与此同时,我们描述了那些吉洪诺夫空间为这 卓著,解决了我们系列论文中的原始问题。