On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane

• Autorzy: G. R. Conner , J. W. Lamoreaux
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 55M15: Absolute neighborhood retracts
• 20E05: Free nonabelian groups
• 57N05: Topology of E 2 , 2 -manifolds
• 54E35: Metric spaces, metrizability
• 57M10: Covering spaces
• 20F34: Fundamental groups and their automorphisms
• 55Q52: Homotopy groups of special spaces
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
• 55Q05: Homotopy groups, general; sets of homotopy classes
• 57M05: Fundamental group, presentations, free differential calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 187
• Numer: 2
• Strony: 95-110

Daty

wydano

2005

Twórcy

autor

G. R. Conner

• Mathematics Department, Brigham Young University, Provo, UT 84602, U.S.A.

autor

J. W. Lamoreaux

• Mathematics Department, Brigham Young University, Provo, UT 84602

Identyfikatory

DOI

10.4064/fm187-2-1