Bøger i Graduate Texts in Mathematics serien

Aimed at graduate math students, this classic work is a systematic exposition of general topology and is intended to be a reference and a text. As a reference, it offers a reasonably complete coverage of the area, resulting in a more extended treatment than normally given in a course.

The term "weakly differentiable functions" in the title refers to those inte n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation.

At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level.

Based on a graduate course at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes.

Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures

The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces.

This work has become the standard introduction to the theory of p-adic numbers. The 2nd edition adds a deeper treatment of p-adic functions, including the Iwasawa logarithm and the p-adic gamma-function, plus new exercises and an appendix of answers and hints.

The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem.

This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra.

This book focuses on complex analytic dynamics, which dates from 1916 and is currently attracting considerable interest. The text provides a comprehensive, well-organized treatment of the foundations of the theory of iteration of rational functions of a complex variable.