In mathematics, upper hemicontinuity and lower hemicontinuity are extensions of the notions of upper and lower semicontinuity of single-valued functions...

multifunctions via continuous functions explains why upper hemicontinuity is more preferred than lower hemicontinuity. Nevertheless, lower semi-continuous multifunctions...

some common metric space L. Wijsman convergence Kuratowski convergence Hemicontinuity Fréchet distance Hypertopology Rockafellar, R. Tyrrell; Wets, Roger...

lower, outer, and inner semicontinuity, as well as upper and lower hemicontinuity. A set-valued function F {\displaystyle F} from a set A {\displaystyle...

topological space Hilbert space – Type of topological vector space Hemicontinuity – Semicontinuity for set-valued functions Linear subspace – In mathematics...

… , V x n {\displaystyle G,V_{x_{1}},\dots ,V_{x_{n}}} . By upper hemicontinuity, there is a neighborhood U θ {\displaystyle U_{\theta }} of θ {\displaystyle...

Axiom of countable choice Axiom of dependent choice Hausdorff paradox Hemicontinuity Zermelo, Ernst (1904). "Beweis, dass jede Menge wohlgeordnet werden...

theorem to an equivalence relating approximate selections to almost lower hemicontinuity, where F {\displaystyle F} is said to be almost lower hemicontinuous...

sources, including Kakutani's original paper, use the concept of upper hemicontinuity while stating the theorem: Let S be a non-empty, compact and convex...

mathematics defined as differential inclusion for non-uniform upper hemicontinuity convex set with compactness in fuzzy set. d x ( t ) / d t = F ( t ,...

set-valued functions is commonly defined in terms of lower- and upper-hemicontinuity popularized by Berge. In this sense, a set-valued function is continuous...

space. Hausdorff distance Kuratowski convergence Vietoris topology Hemicontinuity Notes Wijsman, Robert A. (1966). "Convergence of sequences of convex...