Hyperspaces Topologies Relative Compactness Sup Measures Gap Functional
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 25, No 1, (1999), 11p-18p
The present paper contains results characterizing relatively
compact subsets of the space of the closed subsets of a metrizable space,
equipped with various hypertopologies.
We investigate the hyperspace topologies that admit a representation as
weak topologies generated by families of gap functionals defined on closed
sets, as well as hit-and-miss topologies and proximal-hit and-miss topologies.