Vol. 47, No. 2, 1973

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Composants of Hausdorff indecomposable continua; a mapping approach

David Parham Bellamy

Vol. 47 (1973), No. 2, 303–309

“Continuum” denotes a compact connected Hausdorff space. The principal result is that every indecomposable continuum can be mapped onto Knaster’s example D of a chainable indecomposable continuum with one endpoint. This result is then used to conclude that those indecomposable continua each of whose proper subcontinua is decomposable, those which are homeomorphic with each of their nondegenerate subcontinua, and those such that each two points in the same composant can be joined by a continuum which cannot be mapped onto D, have at least c composants. It is also shown that generalized arcwise connected continua are decomposable.

Mathematical Subject Classification
Primary: 54F20
Received: 21 June 1972
Revised: 30 August 1972
Published: 1 August 1973
David Parham Bellamy