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Introduction to Real Analysis Fall 2014 Lecture Notes

Introduction to real AnalysisFall 2014 Lecture NotesVern I. PaulsenNovember 6, 20142 Contents1 Metric Definition and Examples .. Spaces, Norms and Metrics .. Open Sets .. Equivalent Metrics .. Closed Sets .. Convergent Sequences .. results on convergence inRk.. Interiors, Closures, Boundaries of Sets .. Completeness .. Compact Sets .. 302 Finite and Infinite Sets, Countability373 Continuous Functions into Euclidean space .. Continuity of Some Basic Functions.

Chapter 1 Metric Spaces These notes accompany the Fall 2011 Introduction to Real Analysis course 1.1 De nition and Examples De nition 1.1. Given a set X a metric on X is a function d: X X!R

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