The structure of decomposable snakelike continua

Abstract

The notion of a chainable continuum was introduced by R. L. Moore in [10] (see also [11]); and, in [12], J. H. Roberts showed that any chainable plane continuum has uncountably many disjoint images in the plane. More recently, Moise and Bing used a certain chainable continuum, the pseudo arc, as an example to settle two questions of considerable interest, ([3] and [9]). In [5] Bing defines the notion of a snakelike continuum and shows that it is equivalent to the earlier notion of chainable plane continuum and makes a study of some of the properties of snakelike continua. Recently, Henderson, [7], makes use of the structure of decomposable snakelike continuum to obtain the result that the only decomposable continuum homeomorphic to each of its proper subcontinua is the arc. However, all but one of the fifteen theorems in his paper contain the hypothesis that the set considered is (by his result) an arc.13. W. A. WILSON, On the structure of a continuum, limited and irreducible between two points,

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