A continuous homomorphism of a thin set onto a fat set

Title: A continuous homomorphism of a thin set onto a fat set
Creator: Chalebgwa, Taboka; Morris, Sidney
Date: 2022
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/188608
Identifier: vital:17296
Identifier: https://doi.org/10.1017/S0004972722000296
Identifier: ISSN:0004-9727 (ISSN)
Abstract: A thin set is defined to be an uncountable dense zero-dimensional subset of measure zero and Hausdorff measure zero of an Euclidean space. A fat set is defined to be an uncountable dense path-connected subset of an Euclidean space which has full measure, that is, its complement has measure zero. While there are well-known pathological maps of a set of measure zero, such as the Cantor set, onto an interval, we show that the standard addition on
Publisher: Cambridge University Press
Relation: Bulletin of the Australian Mathematical Society Vol. 106, no. 3 (2022), p. 500-503
Rights: All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
Subject: 49 Mathematical sciences; Hausdorff measure; Lebesgue measure; Liouville numbers
Reviewed

		Thumbnail	File	Description	Size	Format