From Geometry to TopologyCrane, Russak, 1974 - 186 Seiten This introduction to topology eases readers into the subject by building a bridge from the familiar concepts of geometry to the formalized study of topology. Focuses on congruence classes defined by transformations in real Euclidean space, continuity, sets, functions, metric spaces, and topological spaces, more. Exercises and Problems. Includes 101 black-and-white illustrations. 1974 edition. |
Inhalt
Congruence Classes | 1 |
NonEuclidean Geometries | 9 |
From Geometry to Topology | 17 |
Urheberrecht | |
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affine transformations 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 direction disc distance distinct domain drawn elements equal equivalence classes equivalent Euclidean Euler characteristic example expression fact follows formal four function further geometry given gives handles hence holes homeomorphic important included inside integer intersection interval intuitive invariant inverse joined labelled least length line segment mathematics metric necessary neighbourhood obtained once original pair particular path permitted plane diagram polygonal positive possible preserved projective properties regions remain removed representation represented respectively resulting satisfies seen separated shown sides similar simply single sphere subset surface symbolic termed theorem topological space torus transformation triangle vertex vertices