Real Variables: With Basic Metric Space Topology
by Robert B. Ash
Publisher: Institute of Electrical & Electronics Engineering 2007
Number of pages: 213
This is a text for a first course in real variables for students of engineering, physics, and economics, who need to know real analysis in order to cope with the professional literature in their fields. The book tends to avoid standard mathematical writing, with its emphasis on formalism, but a certain amount of abstraction is unavoidable for a coherent presentation.
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by Sidney A. Morris
It provides a thorough grounding in general topology: introduction, topological spaces, the Euclidian topology, limit points, homeomorphisms, continuous mappings, metric spaces, compactness, finite products, countable products, Tychonoff's theorem.
by Allen Hatcher - Cornell University
These are lecture notes from the first part of an undergraduate course in 2005, covering just the most basic things. From the table of contents: Basic Point-Set Topology; Connectedness; Compactness; Quotient Spaces; Exercises.
by Alex Kuronya
Contents: Basic concepts; Constructing topologies; Connectedness; Separation axioms and the Hausdorff property; Compactness and its relatives; Quotient spaces; Homotopy; The fundamental group and some applications; Covering spaces; etc.
by Casper Goffman, at al. - American Mathematical Society
This book features the interplay of two main branches of mathematics: topology and real analysis. The text covers Lebesgue measurability, Baire classes of functions, differentiability, the Blumberg theorem, various theorems on Fourier series, etc.