Author | Guzman, Alberto. author |
---|---|
Title | Continuous Functions of Vector Variables [electronic resource] / by Alberto Guzman |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0083-3 |
Descript | X, 210 p. 16 illus. online resource |
1 Euclidean Space -- 1.1 Multiple Variables -- 1.2 Points and Lines in a Vector Space -- 1.3 Inner Products and the Geometry of Rn -- 1.4 Norms and the Definition of Euclidean Space -- 1.5 Metrics -- 1.6 Infinite-Dimensional Spaces -- 2 Sequences in Normed Spaces -- 2.1 Neighborhoods in a Normed Space -- 2.2 Sequences and Convergence -- 2.3 Convergence in Euclidean Space -- 2.4 Convergence in an Infinite-Dimensional Space -- 3 Limits and Continuity in Normed Spaces -- 3.1 Vector-Valued Functions in Euclidean Space -- 3.2 Limits of Functions in Normed Spaces -- 3.3 Finite Limits -- 3.4 Continuity -- 3.5 Continuity in Infinite-Dimensional Spaces -- 4 Characteristics of Continuous Functions -- 4.1 Continuous Functions on Boxes in Euclidean Space -- 4.2 Continuous Functions on Bounded Closed Subsets of Euclidean Space -- 4.3 Extreme Values and Sequentially Compact Sets -- 4.4 Continuous Functions and Open Sets -- 4.5 Continuous Functions on Connected Sets -- 4.6 Finite-Dimensional Subspaces of Normed Linear Spaces -- 5 Topology in Normed Spaces -- 5.1 Connected Sets -- 5.2 Open Sets -- 5.3 Closed Sets -- 5.4 Interior, Boundary, and Closure -- 5.5 Compact Sets -- 5.6 Compactness in Infinite Dimensions -- Solutions to Exercises -- References