Buch, Englisch, 210 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 341 g
ISBN: 978-0-8176-4273-0
Verlag: Birkhäuser Boston
This is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. The author covers boundedness, extreme values, and uniform continuity of functions, along with connections between continuity and topological concepts such as connectedness and compactness. The order of topics mimics the order of development in elementary calculus, with analogies and generalizations from such familiar ideas as the Pythagorean theorem.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
Weitere Infos & Material
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.
