Waraszkiewicz spirals revisited

Pavel Pyrih, and Benjamin Vejnar. "Waraszkiewicz spirals revisited." Fundamenta Mathematicae 219.2 (2012): 97-104. <http://eudml.org/doc/286300>.

@article{PavelPyrih2012,
abstract = {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).},
author = {Pavel Pyrih, Benjamin Vejnar},
journal = {Fundamenta Mathematicae},
keywords = {continuous map; continuum; incomparability; spiral; uncountable family},
language = {eng},
number = {2},
pages = {97-104},
title = {Waraszkiewicz spirals revisited},
url = {http://eudml.org/doc/286300},
volume = {219},
year = {2012},
}

TY - JOUR
AU - Pavel Pyrih
AU - Benjamin Vejnar
TI - Waraszkiewicz spirals revisited
JO - Fundamenta Mathematicae
PY - 2012
VL - 219
IS - 2
SP - 97
EP - 104
AB - 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).
LA - eng
KW - continuous map; continuum; incomparability; spiral; uncountable family
UR - http://eudml.org/doc/286300
ER -