G. R. Conner, and J. W. Lamoreaux. "On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane." Fundamenta Mathematicae 187.2 (2005): 95-110. <http://eudml.org/doc/282973>.
@article{G2005,
abstract = {We prove several results concerning the existence of universal covering spaces for separable metric spaces. To begin, we define several homotopy-theoretic conditions which we then prove are equivalent to the existence of a universal covering space. We use these equivalences to prove that every connected, locally path connected separable metric space whose fundamental group is a free group admits a universal covering space. As an application of these results, we prove the main result of this article, which states that a connected, locally path connected subset of the Euclidean plane, 𝔼², admits a universal covering space if and only if its fundamental group is free, if and only if its fundamental group is countable.},
author = {G. R. Conner, J. W. Lamoreaux},
journal = {Fundamenta Mathematicae},
keywords = {planar; free group; fundamental group; covering space; metrizable},
language = {eng},
number = {2},
pages = {95-110},
title = {On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane},
url = {http://eudml.org/doc/282973},
volume = {187},
year = {2005},
}
TY - JOUR
AU - G. R. Conner
AU - J. W. Lamoreaux
TI - On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane
JO - Fundamenta Mathematicae
PY - 2005
VL - 187
IS - 2
SP - 95
EP - 110
AB - We prove several results concerning the existence of universal covering spaces for separable metric spaces. To begin, we define several homotopy-theoretic conditions which we then prove are equivalent to the existence of a universal covering space. We use these equivalences to prove that every connected, locally path connected separable metric space whose fundamental group is a free group admits a universal covering space. As an application of these results, we prove the main result of this article, which states that a connected, locally path connected subset of the Euclidean plane, 𝔼², admits a universal covering space if and only if its fundamental group is free, if and only if its fundamental group is countable.
LA - eng
KW - planar; free group; fundamental group; covering space; metrizable
UR - http://eudml.org/doc/282973
ER -
