Extension dimensional approximation theorem

It is known that if an upper semicontinuous multivalued mapping F :X→Y, defined on an n-dimensional compactum X, has UVn−1-point images, then every neighbourhood of the graph of F (in the product X×Y) contains the graph of a single-valued continuous mapping f :X→Y. Similar result is known to be true when X is a compact C-space and images of F have trivial shape. We extend and unify both of these results in terms of extension theory.