Two-to-one maps on solenoids and Knaster continua
It is shown that 2-to-1 maps cannot be defined on certain solenoids, in particular on the dyadic solenoid, and on Knaster continua.
Composant-like decompositions
The body of this paper falls into two independent sections. The first deals with the existence of cross-sections in -decompositions. The second deals with the extensions of the results on accessibility in the plane.
Exactly two-to-one maps from continua onto arc-continua
Continuing studies on 2-to-1 maps onto indecomposable continua having only arcs as proper non-degenerate subcontinua - called here arc-continua - we drop the hypothesis of tree-likeness, and we get some conditions on the arc-continuum image that force any 2-to-1 map to be a local homeomorphism. We show that any 2-to-1 map from a continuum onto a local Cantor bundle Y is either a local homeomorphism or a retraction if Y is orientable, and that it is a local homeomorphism if Y is not orientable.
Exactly two-to-one maps from continua onto some tree-like continua
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...
Perfect sets of independent functions
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