From Geometry to TopologyCourier Corporation, 08.03.2012 - 208 Seiten This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4–12 give a largely intuitive presentation of selected topics. In the remaining five chapters, the author moves to a more conventional presentation of continuity, sets, functions, metric spaces, and topological spaces. Exercises and Problems. 101 black-and-white illustrations. 1974 edition. |
Inhalt
1 | |
9 | |
From Geometry to Topology | 17 |
Surfaces | 20 |
Connectivity | 33 |
Euler Characteristic | 40 |
Networks | 58 |
The Colouring of Maps | 70 |
Fixed Point Theorems | 84 |
Plane Diagrams | 90 |
The Standard Model | 101 |
Continuity | 117 |
The Language of Sets | 125 |
Functions | 134 |
Metric Spaces | 150 |
Topological Spaces | 156 |
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Häufige Begriffe und Wortgruppen
affine transformations apply arcs belong boundary Chapter circle Clearly closed curve collection colours complete concept connected considered continuous corresponding cross curve cylinder defined definition deformed depicted in Figure determine direction disc distance distinct domain drawn elements equal equivalence equivalence classes Euclidean Euler characteristic example expression fact follows four function further geometry given gives handles hence holes homeomorphic important included inside integer intersection interval introduction intuitive invariant inverse joined labelled least length line segment mathematics metric necessary neighbourhood obtained original pair particular path permitted plane diagram polygonal positive possible preserved problems projective properties regions remain removed representation represented respectively resulting satisfies seen separated shown sides similar simply single sphere subset surface termed theorem theory topological space torus transformation triangle vertex vertices