Embedding a circle of trees in the plane
Horace Wiser · Pacific Journal of Mathematics · 1965
Concerning the embedding in the plane of homogeneous proper subcontinua of a 2-manif old, it is shown here that there is an embedding if the continuum is decomposable and the manifold is orientable.The embedding is obtained by constructing an annulus on the manifold containing the continuum in the nonorientable case an annulus or a Mδbius strip containing the continuum may be found.Similar results are obtained for continua on a 2-manifold which have a decomposition into continua with zero 1-dimensional Betti numbers such that the decomposition space is a finite planar graph.This extends the results of [2] concerning the embedding in the plane of homogeneous proper subcontinua of a 2-manifold.Definitions and a summary of other results may be found in [2]