Almost continuous functions with closed graphs
Polishness of weak topologies generated by gap and excess functionals.
Functional characterizations of p-spaces
We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.
On relations approximated by continuous functions
An extension theorem for continuous functions
A remark on almost continuous multifunctions
On determining sets for the class of somewhat continuous functions
An extension theorem for multifunctions and a characterization of complete metric spaces
Tibor Neubrunn (1929 – 1990)
Further characterizations of boundedly UC spaces
Following the paper [BDC1], further relations between the classical topologies on function spaces and new ones induced by hyperspace topologies on graphs of functions are introduced and further characterizations of boundedly spaces are given.
Well-posedness of optimization problems and Hausdorff metric on partial maps
The object of this paper is the Hausdorff metric topology on partial maps with closed domains. This topological space is denoted by . An equivalence of well-posedness of constrained continuous problems is proved. By using the completeness of the Hausdorff metric on the space of usco maps with moving domains, the complete metrizability of is investigated.
Kuratowski convergence on compacta and Hausdorff metric convergence on compacta
This paper completes and improves results of [10]. Let , be two metric spaces and be the space of all -valued continuous functions whose domain is a closed subset of . If is a locally compact metric space, then the Kuratowski convergence and the Kuratowski convergence on compacta coincide on . Thus if and are boundedly compact metric spaces we have the equivalence of the convergence in the Attouch-Wets topology (generated by the box metric of and ) and convergence on ,...
Page 1