Document Type
Lecture
Publication Date
2-16-2005
Abstract
The talk will discuss approximations with constraints on the range and on the support. For any ε > 0, the approximant ��ε of �� (continuous maps defined on a topological space ��) is required to take locally (on neighborhoods) values into finite-dimensional subspaces, and to satisfy the restrictions supₜ∈�� ||��(��) − ��ε(��)|| < ε, ��ε(��) ⊆ co(��(��)), supp(��ε) ⊆ int(supp(��)). The result obtained has very distinct applications: a generalization of the Tietze-Dugundji extension theorem, a new proof of the fixed-point theorem of Schauder-Tikhonov, and a density result with respect to the inductive limit topology.
Relational Format
presentation
Recommended Citation
Timofte, Vlad, "Uniform Approximation Under Constrains for Continuous Vector-Valued Functions" (2005). Analysis Seminar. 53.
https://egrove.olemiss.edu/math_analysis/53
