Special uniform approximations of continuous vector-valued functions.: part 1:: Special approximations in Cx(T)

[摘要] In this paper, we give special uniform approximations of functions u from the spaces C-X (T) and C-infinity (T, X), with elements (u) over bar of the tenser products C-Gamma (T) x X, respectively C-0(T, Gamma) x X, for a topological space T and a Gamma-locally convex space X. We call an approximation special, if u satisfies additional constraints, namely supp v subset of u(-1)(X\{0}) and (u) over bar (T) subset of co(u(T)) (resp. subset of co(u(T) boolean OR {0})). In Section 3, we give three distinct applications, which are due exactly to these constraints: a density result with respect to the inductive limit topology, a Tietze-Dugundji's type extension new theorem and a proof of Schauder-Tihonov's fixed point theorem. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-12-01

[关键词] uniform approximation;tensor product;extension by continuity