Vol. 47, No. 1, 1973

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ISSN: 0030-8730
Aposyndetic properties of hyperspaces

Jack Tilden Goodykoontz, Jr.

Vol. 47 (1973), No. 1, 91–98

Let X be a compact connected metric space and 2X(C(X)) denote the hyperspace of closed subsets (subcontinua) of X. In this paper the hyperspaces are investigated with respect to the property of aposyndesis. The main result states that each of 2X and C(X) is aposyndetic. If X is semi-aposyndetic, then each of 2X and C(X) is mutually aposyndetic. An example is given of a non-semiaposyndetic continuum for which C(X) is not mutually aposyndetic. In an extension of the main result for C(X) it is shown that C(X) is countable closed set aposyndetic. The techniques utilize the partially ordered structure of 2X and C(X).

Mathematical Subject Classification 2000
Primary: 54B20
Secondary: 54F20
Received: 9 March 1972
Revised: 28 June 1972
Published: 1 July 1973
Jack Tilden Goodykoontz, Jr.