Waraszkiewicz spirals revisited
Volume 219 / 2012
Fundamenta Mathematicae 219 (2012), 97-104 MSC: Primary 54F15; Secondary 54F50. DOI: 10.4064/fm219-2-1
We study compactifications of a ray with remainder a simple closed curve. We give necessary and sufficient conditions for the existence of a bijective (resp. surjective) mapping between two such continua. Using those conditions we present a simple proof of the existence of an uncountable family of plane continua no one of which can be continuously mapped onto any other (the first such family, so called Waraszkiewicz's spirals, was created by Z. Waraszkiewicz in the 1930's).