Author | Rado, T. author |
---|---|
Title | Continuous Transformations in Analysis [electronic resource] : With an Introduction to Algebraic Topology / by T. Rado, P. V. Reichelderfer |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1955 |
Connect to | http://dx.doi.org/10.1007/978-3-642-85989-2 |
Descript | VIII, 442 p. 2 illus. online resource |
I. Background in Topology -- ยง I.1. Survey of general topology -- ยง I.2. Survey of Euclidean spaces -- ยง I.3. Survey of Abelian groups -- ยง I.4. Mayer complexes -- ยง I.5. Formal complexes -- ยง I.6. General cohomology theory -- ยง I.7. Cohomology groups in Euclidean spaces -- II. Topological study of continuous transformations in Rn -- ยง II.1. Orientation in Rn -- ยง II.2. The topological index -- ยง II.3. Multiplicity functions and index functions -- III. Background in Analysis -- ยง III.1. Survey of functions of real variables -- ยง III.2. Functions of open intervals in Rn -- IV. Bounded variation and absolute continuity in Rn -- ยง IV.1. Measurability questions -- ยง IV.2. Bounded variation and absolute continuity with respect to a base-function -- ยง IV.3. Bounded variation and absolute continuity with respect to a multiplicity function -- ยง IV.4. Essential bounded variation and absolute continuity -- ยง IV.5. Bounded variation and absolute continuity in the Banach sense -- V. Differentiable transformations in Rn -- ยง V.1. Continuous transformations in R1 -- ยง V.2. Local approximations in Rn -- ยง V.3. Special classes of differentiable transformations in Rn -- VI. Continuous transformations in R2 -- ยง VI.1. The topological index in R2 -- ยง VI.2. Special features of continuous transformations in R2 -- ยง VI.3. Special classes of differentiable transformations in R2