Media Summary: Weak compactness and weak sequential compactness. Uniformly convex spaces. Examples and other equivalent ... Review of normed spaces and linear bounded operators. The dual of a normed space. Examples of dual spaces. Definition and some basic properties of the weak topology and weak convergence.
Math400 Functional Analysis Section 4 6 And 4 7 - Detailed Analysis & Overview
Weak compactness and weak sequential compactness. Uniformly convex spaces. Examples and other equivalent ... Review of normed spaces and linear bounded operators. The dual of a normed space. Examples of dual spaces. Definition and some basic properties of the weak topology and weak convergence. Exercises on total boundedness and equicontinuity. Other characterizations of reflexivity. Illustration of the use of reflexivity in the calculus of variations. Definition and examples of separable metric spaces and Banach spaces. Separability of the dual implies separability of the space.
Construction and properties of the smallest topology making continuous a collection of maps. Definition and examples of topological spaces. The subspace topology. Comparison of topologies. Bases
