ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: António Lopes-Pinto & Diana Mendes Representation of Multivalued Maps The problem of representation of set-valued mappings is solved in the framework of the lower semicontinuity. “Let X, Y and Z be topological spaces, f: X × Y Z be a separately continuous single-valued function and Γ: X 2^{Z} \ ∅ be a set-valued mapping. Assume f (x, Y) ∩ Γ (x) ≠ ∅, x ∈ X. There exists a lower semicontinuous set-valued function H: X 2^{Y} \ ∅ such that f(x, H (x)) ⊆ Γ (x) , x ∈ X ? ” This question deals directly with the lower semicontinuity criteria for the regulation map in Control Theory and Viability Theory.