Vol. 53, No. 1, 1974

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Hyperspaces of graphs are Hilbert cubes

Richard Miles Schori and James Edward West

Vol. 53 (1974), No. 1, 239–251

The authors prove tbat 2Γ is a Hilbert cube where Γ is any nondegenerate, finite, connected graph and 2Γ is the space of nonvoid closed subsets of Γ metrized with the Hausdorff metric. This extends their result that 2t is a Hilbert cube. They also prove corresponding theorems for local dendrons D as well as for the space of subcontinua C(D) of D.

Mathematical Subject Classification 2000
Primary: 54B20
Received: 15 June 1973
Published: 1 July 1974
Richard Miles Schori
James Edward West