Characterizing chainable, tree-like, and circle-like continua
Colloquium Mathematicum, Tome 124 (2011) no. 1, pp. 1-13
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that a continuum $X$ is tree-like (resp. circle-like, chainable) if and only if for each open cover $\mathcal U_4=\{U_1,U_2,U_3,U_4\}$ of $X$ there is a $\mathcal U_4$-map $f\colon X\to Y$ onto a tree (resp. onto the circle, onto the interval). A continuum $X$ is an acyclic curve if and only if for each open cover $\mathcal U_3=\{U_1,U_2,U_3\}$ of $X$ there is a $\mathcal U_3$-map $f\colon X\to Y$ onto a tree (or the interval $[0,1]$).
Keywords:
prove continuum tree like resp circle like chainable only each cover mathcal there mathcal map colon tree resp circle interval continuum acyclic curve only each cover mathcal there mathcal map colon tree interval
Affiliations des auteurs :
Taras Banakh 1 ; Zdzisław Kosztołowicz 2 ; Sławomir Turek 3
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author = {Taras Banakh and Zdzis{\l}aw Koszto{\l}owicz and S{\l}awomir Turek},
title = {Characterizing chainable, tree-like, and circle-like continua},
journal = {Colloquium Mathematicum},
pages = {1--13},
publisher = {mathdoc},
volume = {124},
number = {1},
year = {2011},
doi = {10.4064/cm124-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-1/}
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TY - JOUR AU - Taras Banakh AU - Zdzisław Kosztołowicz AU - Sławomir Turek TI - Characterizing chainable, tree-like, and circle-like continua JO - Colloquium Mathematicum PY - 2011 SP - 1 EP - 13 VL - 124 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-1/ DO - 10.4064/cm124-1-1 LA - en ID - 10_4064_cm124_1_1 ER -
%0 Journal Article %A Taras Banakh %A Zdzisław Kosztołowicz %A Sławomir Turek %T Characterizing chainable, tree-like, and circle-like continua %J Colloquium Mathematicum %D 2011 %P 1-13 %V 124 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-1/ %R 10.4064/cm124-1-1 %G en %F 10_4064_cm124_1_1
Taras Banakh; Zdzisław Kosztołowicz; Sławomir Turek. Characterizing chainable, tree-like, and circle-like continua. Colloquium Mathematicum, Tome 124 (2011) no. 1, pp. 1-13. doi: 10.4064/cm124-1-1
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