Vol. 42, No. 2, 1972

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Planar images of decomposable continua

Charles Lemuel Hagopian

Vol. 42 (1972), No. 2, 329–331

A nondegenerate metric space that is both compact and connected is called a continuum. In this paper it is proved that if M is a continuum with the property that for each indecomposable subcontinuum H of M there is a continuum K in M containing H such that K is connected im kleinen at some point of H and if f is a continuous function on M into the plane, then the boundary of each complementary domain of f(M) is hereditarily decomposable. Consequently, if M is a continuum in Euclidean n-space that does not contain an indecomposable continuum in its boundary, then no planar continuous image of M has an indecomposable continuum in the boundary of one of its complementary domains.

Mathematical Subject Classification
Primary: 54F20
Secondary: 57A05
Received: 17 June 1971
Revised: 7 September 1971
Published: 1 August 1972
Charles Lemuel Hagopian