CL(R) is simply connected under the Vietoris topology

N.C. Esty


In this paper we present a proof by construction that the hyperspace CL(R) of closed, nonemtpy subsets of R is simply connected under the Vietoris topology. This is useful in considering the convergence of time scales. We also present a construction of the (known) fact that this hyperspace is also path connected, as part of the proof.


Hyperspace; Vietoris topology; Simply connected; Path connected; Time scales

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Topology and its Applications  vol: 196  first page: 795  year: 2015  
doi: 10.1016/j.topol.2015.05.022

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