Real numbers with redundant representations
type: Item
instance of: scholarly article
title: Real numbers with redundant representations
zbMATH Open document ID: 0760.40001
published in: Real Analysis Exchange
publication date: 1992-09-26T00:00:00Z
review text: Let \((P_ j)\) be a sequence of sets \(P_ j\) of real numbers such that each set is countable and has more than one point. Put \(A=\{x\): \(x=\sum_{j=1}^{+\infty} a_ j\) (\(a_ j\in P_ j\)) uniquely\(\}\) and \(B=\{y\): \(y=\sum_{j=1}^{+\infty} b_ j=\sum_{j=1}^{+\infty} c_ j\) (\(b_ j,c_ j\in P_ j\), \((b_ j)\neq (c_ j)\}\). Unifying and generalizing results by M. Petkovsek and M. Starbird and T. Starbird, the author proves that if the set \(A\cup B\) is of the second category, then \(A\cup B\subset \text{cl}(B)\) (the closure of \(B\)).
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 11A67
zbMATH DE Number: 54508
zbMATH Keywords: representation of real numbers
zbMATH Keywords: dense and second category subsets of \(R\)
author: Frank S. Cater
reviewed by: József Sándor
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 54508