On some Generic Small Cantor Spaces

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2020-07-06 DOI:10.4171/ZAA/1660

E. D’Aniello, M. Maiuriello

引用次数: 0

Abstract

Let $X = [0,1]^{n}$, $n \geq1$. We show that the typical (in the sense of Baire category) compact subset of $X$ is not only a zero dimensional Cantor space but it satisfies the property of being strongly microscopic, which is stronger than being of dimension zero.

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关于一些一般小康托空间

让$X = [0,1]^{n}$, $n \geq1$。证明了$X$的典型(在Baire范畴意义上)紧子集不仅是零维康托空间，而且满足强微观的性质，强微观的性质强于零维康托空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.