CL(R) is simply connected under the Vietoris topology

N.C. Esty

Abstract

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.


Keywords

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

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References

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