Homeomorphisms in Analysis
by Casper Goffman, at al.
Publisher: American Mathematical Society 1997
Number of pages: 216
This book features the interplay of two main branches of mathematics: topology and real analysis. The material of the book is largely contained in the research publications of the authors and their students from the past 50 years. Parts of analysis are touched upon in a unique way, for example, Lebesgue measurability, Baire classes of functions, differentiability, the Blumberg theorem, bounded variation in the sense of Cesari, and various theorems on Fourier series and generalized bounded variation of a function.
Home page url
Download or read it online for free here:
by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov - American Mathematical Society
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space.
by John McCleary - American Mathematical Society
A focused introduction to point-set topology, the fundamental group, and the beginnings of homology theory. The text is intended for advanced undergraduate students. It is suitable for students who have studied real analysis and linear algebra.
by T. W. Körner - University of Cambridge
Contents: What is a metric?; Examples of metric spaces; Continuity and open sets for metric spaces; Closed sets for metric spaces; Topological spaces; Interior and closure; More on topological structures; Hausdorff spaces; Compactness; etc.
by Victor Porton - Mathematics21.org
I introduce the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces. Funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details concept of uniformity.