Exactly two-to-one maps from continua onto some tree-like continua. (English) Zbl 0807.54015

Summary: It is known that no dendrite [W. H. Gottschalk, Bull. Am. Math. Soc. 53, 168-169 (1947; Zbl 0040.254)] and no hereditarily indecomposable tree-like continuum [J. Heath, Proc. Am. Math. Soc. 113, No. 3, 839-846 (1991; Zbl 0738.54012)] 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. B. Nadler jun. and L. E. Ward jun., ibid. 87, 351-354 (1983; Zbl 0503.54018)], is still neither confirmed nor rejected.


54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54F15 Continua and generalizations
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