Geodesic
Waraszkiewicz spirals revisited
Pavel Pyrih 1   ; Benjamin Vejnar 1
1 Faculty of Mathematics and Physics Charles University Sokolovská 83 CZ-186 75 Praha 8, Czech Republic
Fundamenta Mathematicae, Tome 219 (2012) no. 2, pp. 97-104 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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).
DOI : 10.4064/fm219-2-1
Mots-clés : study compactifications ray remainder simple closed curve necessary sufficient conditions existence bijective resp surjective mapping between continua using those conditions present simple proof existence uncountable family plane continua which continuously mapped other first family called waraszkiewiczs spirals created nbsp waraszkiewicz

Pavel Pyrih  1   ; Benjamin Vejnar  1

1 Faculty of Mathematics and Physics Charles University Sokolovská 83 CZ-186 75 Praha 8, Czech Republic 
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Pavel Pyrih; Benjamin Vejnar. Waraszkiewicz spirals revisited. Fundamenta Mathematicae, Tome 219 (2012) no. 2, pp. 97-104. doi: 10.4064/fm219-2-1

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