Vol. 25, No. 2, 1968

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Quasi dimension type. II. Types in 1-dimensional spaces

Jack Segal

Vol. 25 (1968), No. 2, 353–370

In this paper we consider the partial ordering induced on 1-dimensional continua by quasi dimension type. For example, we show that the pseudo-arc precedes every snake-like continuum in this partial ordering. We also obtain sufficient conditions in terms of quasi dimension type for the embedding of Peano continua in the plane. Finally, necessary and sufficient conditions in terms of quasi dimension type are given for a continuum to be tree-like and to be 1-dimensional.

Mathematical Subject Classification
Primary: 54.70
Received: 26 October 1964
Revised: 2 August 1967
Published: 1 May 1968
Jack Segal