当前位置: X-MOL 学术J. Fourier Anal. Appl. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On Sets Containing an Affine Copy of Bounded Decreasing Sequences
Journal of Fourier Analysis and Applications ( IF 1.2 ) Pub Date : 2020-09-09 , DOI: 10.1007/s00041-020-09780-4
Tongou Yang

How small can a set be while containing many configurations? Following up on earlier work of Erdős and Kakutani (Colloq Math 4:195–196, 1957), Máthé (Fund Math 213(3):213–219, 2011) and Molter and Yavicoli (Math Proc Camb Soc 168:57–73, 2018), we address the question in two directions. On one hand, if a subset of the real numbers contains an affine copy of all bounded decreasing sequences, then we show that such a subset must be somewhere dense. On the other hand, given a collection of convergent sequences with prescribed decay, there is a closed and nowhere dense subset of the reals that contains an affine copy of every sequence in that collection.

中文翻译:

关于包含有界递减序列的仿射副本的集合

包含许多配置的集合可以有多小?跟进Erdős和Kakutani(Colloq Math 4:195–196,1957),Máthé(Fund Math 213(3):213–219,2011)和Molter and Yavicoli(Math Proc Camb Soc 168:57–73)的早期工作(2018年),我们从两个方向解决这个问题。一方面,如果实数的一个子集包含所有有界递减序列的仿射副本,那么我们表明该子集必须在某处密集。另一方面,给定具有规定衰减的收敛序列的集合,实部的封闭且无处密集的子集包含该集合中每个序列的仿射副本。
更新日期:2020-09-09
down
wechat
bug