Waraszkiewicz spirals revisited

• Autorzy: Pavel Pyrih , Benjamin Vejnar
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites
• 54F15: Continua and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 219
• Numer: 2
• Strony: 97-104

Daty

wydano

2012

Twórcy

autor

Pavel Pyrih

• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, CZ-186 75 Praha 8, Czech Republic

autor

Benjamin Vejnar

• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, CZ-186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/fm219-2-1