Metric and Topological Spaces I

Igor Kriz and Aleš Pultr
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Igor Kriz: University of Michigan, Department of Mathematics
Aleš Pultr: Charles University, Department of Applied Mathematics (KAM) Faculty of Mathematics and Physics

Chapter 2 in Introduction to Mathematical Analysis, 2013, pp 33-63 from Springer

Abstract: 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.

Date: 2013
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DOI: 10.1007/978-3-0348-0636-7_2

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