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Abstract We show that for any map f on an arc-like continuum X, the induced map f ˆ on the hyperspace of subcontinua C ( X ) fixes a point… Click to show full abstract
Abstract We show that for any map f on an arc-like continuum X, the induced map f ˆ on the hyperspace of subcontinua C ( X ) fixes a point in any f ˆ -invariant subcontinuum of C ( X ) . This extends a result of Robatian [21] , who proved it for the arc. However, as we show, the result does not extend to tree-like continua. We conclude with a list of related problems. Our proof builds on Hamilton's proof of the fixed point property of arc-like continua [12] .
Keywords:
sternbach type;
type fixed;
point;
point problem;
problem maps;
fixed point
Journal Title: Topology and its Applications
Year Published: 2020
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Journal Title: Topology and its Applications
Year Published: 2020
Link to full text (if available)
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recommendations!