Abstract
We investigate joint upper and lower semicontinuity of two-variable set-valued functions. More precisely, among other results, we show that, under certain conditions, a two-variable lower horizontally quasicontinuous mapping F : X × Y → K(Z) is jointly upper semicontinuous on sets of the form D × {y0}, where D is a dense G𝛿 -subset of X and y0 ∈ Y. A similar result was obtained for the joint lower semicontinuity of upper horizontally quasicontinuous mappings. These results improve some known results on the joint continuity of single-valued functions.
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