Vol. 15, No. 4, 1965

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Embedding a circle of trees in the plane

Horace C. Wiser

Vol. 15 (1965), No. 4, 1463–1464

Concerning the embedding in the plane of homogeneous proper subcontinua of a 2-manifold, 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 Möbius 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.

Mathematical Subject Classification
Primary: 55.10
Secondary: 05.50
Received: 16 September 1964
Published: 1 December 1965
Horace C. Wiser