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Exactly two-to-one maps from continua onto some tree-like continua

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Dębski W., Heath J., Mioduszewski J.

Fundamenta Mathematicae

1992

tom 141

nr 3

269-276

It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua and Ingram continua. The conjecture that all tree-like continua have this property, stated by S. Nadler Jr. and L. E. Ward Jr. (1983), is still neither confirmed nor rejected.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Dębski W.

1 Heath J.

1 Mioduszewski J.

1 1992

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Exactly two-to-one maps from continua onto some tree-like continua