Vol. 108, No. 1, 1983

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On the convergence of closed and compact sets

Eva Lowen-Colebunders

Vol. 108 (1983), No. 1, 133–140

For a topological Hausdorff space X we study the hyperspaces 𝒫(X), 2X and 𝒞(X) of all closed subsets, all non-empty closed subsets and all non-empty compact subsets endowed with the convergence of sets. In this paper we shall work with the filter description of this convergence, as defined by Choquet [2], which however is equivalent to the topological convergence of nets of sets as defined by Frolik and Mrówka. We shall study the relation between properties of X and properties of the spaces 𝒫(X), 2X and 𝒞(X) such as compactness, local compactness, regularity and the topological and pretopological character.

Mathematical Subject Classification 2000
Primary: 54A20
Secondary: 54B20
Received: 4 October 1979
Revised: 26 July 1982
Published: 1 September 1983
Eva Lowen-Colebunders