Geodesic
Exactly two-to-one maps from continua onto some tree-like continua
Fundamenta Mathematicae, Tome 141 (1992) no. 3, pp. 269-276.

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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.
DOI : 10.4064/fm-141-3-269-276
Mots-clés : Knaster continua, Ingram continua, 2-to-1 map

Wojciech Dębski 1 ; J. Heath 1 ; J. Mioduszewski 1

1 
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Wojciech Dębski; J. Heath; J. Mioduszewski. Exactly two-to-one maps from continua onto some tree-like continua. Fundamenta Mathematicae, Tome 141 (1992) no. 3, pp. 269-276. doi : 10.4064/fm-141-3-269-276. https://geodesic-test.mathdoc.fr/articles/10.4064/fm-141-3-269-276/

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