Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 24, No 1, (1998), 49p-72p
A theorem proved by Fort in 1951 says that an upper or lower
semi-continuous set-valued mapping from a Baire space A into non-empty
compact subsets of a metric space is both lower and upper semi-continuous
at the points of a dense Gδ -subset of A.
In this paper we show that the conclusion of Fort’s theorem holds under
the weaker hypothesis of either upper or lower quasi-continuity. The
existence of densely defined continuous selections for lower quasi-continuous
mappings is also proved.
∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.