3-connected Planar Spaces Uniquely Embed in the Sphere
نویسندگان
چکیده
We characterize those locally connected subsets of the sphere that have a unique embedding in the sphere — i.e., those for which every homeomorphism of the subset to itself extends to a homeomorphism of the sphere. This implies that if Ḡ is the closure of an embedding of a 3-connected graph in the sphere such that every 1-way infinite path in G has a unique accumulation point in Ḡ, then Ḡ has a unique embedding in the sphere. In particular, the standard (or Freudenthal) compactification of a 3-connected planar graph embeds uniquely in the sphere.
منابع مشابه
Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
متن کاملExtrinsic sphere and totally umbilical submanifolds in Finsler spaces
Based on a definition for circle in Finsler space, recently proposed by one of the present authors and Z. Shen, a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field, if and only if its circles coincide with circles of the ambient...
متن کاملPlanarity Testing of Graphs on Base of a Spring Model
It is well known that planar embeddings of 3-connected graphs are uniquely determined up to isomorphy of the induced complex of nodes, edges and faces of the plane or the 2-sphere [1]. Moreover, each of the isomorphy classes of these embeddings contains a representative that has a convex polygon as outer border and has all edges embedded as straight lines. We fixate the outer polygon of such em...
متن کاملOn planarity of compact, locally connected, metric spaces
Thomassen [Combinatorica 24 (2004), 699–718] proved that a 2–connected, compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it does not contain K5 or K3,3. The “thumbtack space” consisting of a disc plus an arc attaching just at the centre of the disc shows the assumption of 2–connectedness cannot be dropped. In this work, we introduce “generalized t...
متن کاملQuantification of partial volume effects in planar imaging
Introduction: The limited resolution of the imaging system causes partial volume effects (PVEs). These results in spreading of image counts to the neighboring pixels. This phenomenon is called spill-out effect. This study aimed at quantifying PVEs using ImageJ. Methods:Technetium-99m solution of concentration of 74 kBq/ml was filled into spheres A, B<...
متن کامل