ABSTRACT
Lemma 7.1. The space C(J X [a,b]) equipped with the system (7.3) of seminorms is a locally convex complete metric space. A sequence XJc E C(J X [a,b]) converges to x E C(J X [a,b]) if and only if the restriction zJcIJ" X[CI,6) converges to ZIJ"X[CI,6) in C(Jn X [a, b)) for each n. MoreoverJ a subset M ~ C(J X [a,b]) is bounded (precompact) if and only if each restricted set {zIJ"x[CI,bl : z E M} is a bounded (respectively precompact) subset of C( I n X la, b]).
