CL(R) is simply connected under the Vietoris topology


  • N.C. Esty Marshall University



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


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.


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Author Biography

N.C. Esty, Marshall University

Department of Mathematics


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How to Cite

N. Esty, “CL(R) is simply connected under the Vietoris topology”, Appl. Gen. Topol., vol. 8, no. 2, pp. 259–265, Oct. 2007.



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