Download e-book for iPad: Elementary Point-Set Topology: A Transition to Advanced by Andre L. Yandl,Adam Bowers

By Andre L. Yandl,Adam Bowers

as well as serving as an creation to the fundamentals of point-set topology, this article bridges the distance among the ordinary calculus series and higher-level arithmetic classes. The flexible, unique method specializes in studying to learn and write proofs instead of protecting complex themes. according to lecture notes that have been built over decades on the collage of Seattle, the remedy is aimed at undergraduate math majors and compatible for numerous introductory classes.
Starting with hassle-free thoughts in good judgment and uncomplicated strategies of facts writing, the textual content defines topological and metric areas and surveys continuity and homeomorphism. extra topics contain product areas, connectedness, and compactness. the ultimate bankruptcy illustrates topology's use in different branches of arithmetic with proofs of the basic theorem of algebra and of Picard's life theorem for differential equations.
"This is a back-to-basics introductory textual content in point-set topology which may double as a transition to proofs path. The writing is especially transparent, now not too concise or too wordy. each one component to the e-book ends with numerous workouts. The not obligatory first bankruptcy covers set idea and evidence tools; if the scholars already understand this fabric you can begin with bankruptcy 2 to offer a instantly topology direction, in a different way the ebook can be utilized as an creation to proofs direction also." — Mathematical organization of America

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