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

Tom 141 / 1992

Wojciech Dębski, J. Heath, J. Mioduszewski Fundamenta Mathematicae 141 (1992), 269-276 DOI: 10.4064/fm-141-3-269-276

Streszczenie

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.

Autorzy

  • Wojciech Dębski
  • J. Heath
  • J. Mioduszewski

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