A Fixed Point Theorem for Hyperspaces of λ Connected Continua
Copyright policy )A Fixed Point Theorem for Hyperspaces of λ Connected Continua
Suppose that the hyperspace of compact connected subsets C ( X ) \mathcal {C}(X) of a λ \lambda connected continuum X X can be ϵ \epsilon -mapped (for each ϵ > 0 \epsilon > 0 ) into the plane. We prove that X X is either arc-like or circle-like. It follows from this theorem and results of J. T. Rogers, Jr. and J. Segal that C ( X ) \mathcal {C}(X) has the fixed point property.
Continua and generalizations, Fixed-point and coincidence theorems (topological aspects), Special maps on topological spaces (open, closed, perfect, etc.), Hyperspaces in general topology, Continuous maps, Unicoherence, multicoherence
Continua and generalizations, Fixed-point and coincidence theorems (topological aspects), Special maps on topological spaces (open, closed, perfect, etc.), Hyperspaces in general topology, Continuous maps, Unicoherence, multicoherence
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