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These notes are an introduction to set theory and topology. They are the result of teaching a two-semester course sequence on these topics for many years at Washington University in St. Louis. Typically the students were advanced undergraduate mathematics majors, a few beginning graduate students in mathematics, and some graduate students from other areas that included economics and engineering.
The usual background for the material is an introductory undergraduate analysis course, mostly because it provides a solid introduction to Euclidean space Rn and practice with rigorous arguments — in particular, about continuity. Strictly speaking, however, the material is mostly self-contained. Examples are taken now and then from analysis, but they are not logically necessary for the development of the material. The only real prerequisite is the level of mathematical interest, maturity and patience needed to handle abstract ideas and to read and write careful proofs. A few very capable students have taken this course before introductory analysis (even, rarely, outstanding university freshmen) and invariably they have commented later on how material eased their way into analysis.
Washington University in St. Louis
Saint Louis, Missouri
Mathematics | Set Theory
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Introduction to Set Theory and Topology, Ronald C. Freiwald, Washington University in St. Louis, http://dx.doi.org/10.7936/K7D798QH