On Sets Containing an Affine Copy of Bounded Decreasing Sequences
Classical Analysis and ODEs
2020-10-27 v2
Abstract
How small can a set be while containing many configurations? Following up on earlier work of Erd\H os and Kakutani \cite{MR0089886}, M\'ath\'e \cite{MR2822418} and Molter and Yavicoli \cite{Molter}, 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 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.
Cite
@article{arxiv.1901.06429,
title = {On Sets Containing an Affine Copy of Bounded Decreasing Sequences},
author = {Tongou Yang},
journal= {arXiv preprint arXiv:1901.06429},
year = {2020}
}