Topological Spaces
From Distance to Neighborhood
(Sprache: Englisch)
Topological Spaces: From Distance to Neighborhood is a gentle introduction to topological spaces leading the reader to understand the notion of what is importantin topology vis-a-vis geometry and analysis. The authors have carefully divided the book into...
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Topological Spaces: From Distance to Neighborhood is a gentle introduction to topological spaces leading the reader to understand the notion of what is importantin topology vis-a-vis geometry and analysis. The authors have carefully divided the book into three sections; The line and the plane, Metric spaces and Topological spaces, in order to mitigate the move into higher levels of abstraction. Students are thereby informally assisted in getting aquainted with new ideas while remaining on familiar territory. The authors have also restricted the mathematical vocabulary in the book to avoid overwhelming the reader with the extensive array of technical terms indicating the properties of topological spaces. Additionally, the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration. The intial pace makes the first nine sections into a balanced course in metric spaces while allowing ample material for a two-semester course. The authors do not assume previous knowledge of axiomatic approach or set theory.
Inhaltsverzeichnis zu „Topological Spaces “
- Preface- The Line and the Plane. What Topology is about
...Axioms for R.
...Convergent sequences and continuity
...Curves in the plane
- Metric Spaces. Metrics
...Open and closed sets
...Completeness
...Uniform convergence
...Sequential compactness
...Convergent nets
...Transition to Topology
- Topological Spaces. Topological spaces
...Compactness and the Hausdorff property
...Products and quotients
...The Hahn-Tietze-Tong-Urysohn Theorems
...Connectedness
...Tychonoff's Theorem
- Postscript. A Smorgasbord for further study
...Countable sets
- A Farewell to the Reader
- Literature
- Index of Symbols
- Index of Terms.
Bibliographische Angaben
- Autoren: Gerard Buskes , Arnoud van Rooij
- 1997, 313 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387949941
- ISBN-13: 9780387949949
- Erscheinungsdatum: 15.08.1997
Sprache:
Englisch
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