Range closure extension of input-output relations of topological general systems
Ranks for baire multifunctions
Various ordinal ranks for Baire-1 real-valued functions, which have been used in the literature, are adapted to provide ranks for Baire-1 multifunctions. A new rank is also introduced which, roughly speaking, gives an estimate of how far a Baire-1 multifunction is from being upper semicontinuous.
Regularization of closed-valued multifunctions in a non-metric setting
Related fixed points for set-valued mappings on two uniform spaces.
Relations approximated by continuous functions in the Vietoris topology
Let X be a Tikhonov space, C(X) be the space of all continuous real-valued functions defined on X, and CL(X×ℝ) be the hyperspace of all nonempty closed subsets of X×ℝ. We prove the following result: Let X be a locally connected locally compact paracompact space, and let F ∈ CL(X×ℝ). Then F is in the closure of C(X) in CL(X×ℝ) with the Vietoris topology if and only if: (1) for every x ∈ X, F(x) is nonempty; (2) for every x ∈ X, F(x) is connected; (3) for every isolated x ∈ X, F(x) is a singleton...
Relaxation theorem for set-valued functions with decomposable values
Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has . Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.
Remark on completely Baire-additive families in analytic spaces
Remarks on Hausdorff continuous multifunction and selections
Repulsive Fixed Points of Multivalued Transformations and the Fixed Point Index.
Saddle point theorems on generalized convex spaces.
Scorza Dragoni type theorems
Selections and near-selections in metric linear spaces without local convexity
We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.
Selections of set-valued stochastic processes.
Semicontinuity of maps which are limits of sequences of Baire continuous multivalued maps
Semicontinuity of maps which are limits of sequences of quasi-continuous maltivalued maps
Semi-continuity of set-valued monotone mappings
Semilocal connectedness of product spaces and -continuity of maps.
Set-valued mappings on metric spaces
Set-valued maps with fixed and coincidence points.
Simplicial approximation of small multifunctions