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 Sergio Salbany, Todor Todorov - arXiv
We present Nonstandard Analysis in the framework of the superstructure of a given infinite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics seem to be new in the literature.
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 StevenHurder, DaveMarker - University of Illinois at Chicago
These notes are a supplement for the 'standard undergraduate course' in Analysis. The aim is to present a more general perspective on the incipient ideas of topology encountered when exploring the rigorous theorem-proof approach to Calculus.