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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-2-1,
author = {Pavel Pyrih and Benjamin Vejnar},
title = {Waraszkiewicz spirals revisited},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {97-104},
zbl = {1270.54036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-2-1}
}
Pavel Pyrih; Benjamin Vejnar. Waraszkiewicz spirals revisited. Fundamenta Mathematicae, Tome 219 (2012) pp. 97-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-2-1/