| Abstract: | The paper deals with the essentiality of the convexity condition in the well-known selection theorems due to E. Michael. It
is proved that the convexity of the range of a lower semi-continuous multivalued mapping may be replaced by an essentially
weaker assumption: each value of the multivalued mapping is a graph of a Lipschitzian function of n variables in a suitable
coordinate system. Bibliography: 3 titles.
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 18, pp. 236–252, 1995. |
