Hyperspaces of graphs are Hilbert cubes

Richard Miles Schori and James Edward West

Vol. 53 (1974), No. 1, 239–251

DOI: 10.2140/pjm.1974.53.239

Abstract

The authors prove tbat 2^Γ is a Hilbert cube where Γ is any nondegenerate, finite, connected graph and 2^Γ is the space of nonvoid closed subsets of Γ metrized with the Hausdorff metric. This extends their result that 2^t 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

Milestones

Received: 15 June 1973

Published: 1 July 1974