Characterizing chainable, tree-like, and circle-like continua

Taras Banakh, Zdzisław Kosztołowicz, and Sławomir Turek. "Characterizing chainable, tree-like, and circle-like continua." Colloquium Mathematicae 124.1 (2011): 1-13. <http://eudml.org/doc/283770>.

@article{TarasBanakh2011,
abstract = {We prove that a continuum X is tree-like (resp. circle-like, chainable) if and only if for each open cover 𝓤₄ = \{U₁,U₂,U₃,U₄\} of X there is a 𝓤₄-map f: X → 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 𝓤₃ = \{U₁,U₂,U₃\} of X there is a 𝓤₃-map f: X → Y onto a tree (or the interval [0,1]).},
author = {Taras Banakh, Zdzisław Kosztołowicz, Sławomir Turek},
journal = {Colloquium Mathematicae},
keywords = {chainable continuum; tree-like continuum; circle-like continuum},
language = {eng},
number = {1},
pages = {1-13},
title = {Characterizing chainable, tree-like, and circle-like continua},
url = {http://eudml.org/doc/283770},
volume = {124},
year = {2011},
}

TY - JOUR
AU - Taras Banakh
AU - Zdzisław Kosztołowicz
AU - Sławomir Turek
TI - Characterizing chainable, tree-like, and circle-like continua
JO - Colloquium Mathematicae
PY - 2011
VL - 124
IS - 1
SP - 1
EP - 13
AB - We prove that a continuum X is tree-like (resp. circle-like, chainable) if and only if for each open cover 𝓤₄ = {U₁,U₂,U₃,U₄} of X there is a 𝓤₄-map f: X → 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 𝓤₃ = {U₁,U₂,U₃} of X there is a 𝓤₃-map f: X → Y onto a tree (or the interval [0,1]).
LA - eng
KW - chainable continuum; tree-like continuum; circle-like continuum
UR - http://eudml.org/doc/283770
ER -