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Metric and Topological Spaces I

In: Introduction to Mathematical Analysis

Author

Listed:
  • Igor Kriz

    (University of Michigan, Department of Mathematics)

  • Aleš Pultr

    (Charles University, Department of Applied Mathematics (KAM) Faculty of Mathematics and Physics)

Abstract

A key to rigorous multivariable calculus is a basic understanding of point set topology in the framework of metric spaces. Covering these basic concepts is the purpose of this chapter. We will see that studying these concepts in detail will really pay off in the chapters below. While studying metric spaces, we will discover certain concepts which are independent of metric, and seem to beg for a more general context. This is why, in the process, we will introduce topological spaces as well.

Suggested Citation

  • Igor Kriz & Aleš Pultr, 2013. "Metric and Topological Spaces I," Springer Books, in: Introduction to Mathematical Analysis, edition 127, chapter 2, pages 33-63, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0636-7_2
    DOI: 10.1007/978-3-0348-0636-7_2
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