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Prerequisites: Sets, Algebraic Systems and Classical Analysis Read chapter Read first chapter

2022 | OriginalPaper | Chapter

6. Real-Valued Continuous Functions

Authors : Avishek Adhikari, Mahima Ranjan Adhikari

Published in: Basic Topology 1

Publisher: Springer Nature Singapore

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Abstract

This chapter continues the study of continuous functions from a topological space to the real line space \( \mathbf{R}, \) called the real-valued continuous functions, or, simply, real functions; such functions play a central role in topology and analysis. This chapter also studies uniform convergence of real-valued functions and characterizes normal spaces through separation by real-valued continuous functions.

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previous chapter Compactness and Connectedness
next chapter Countability, Separability and Embedding
Literature
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Adhikari, M.R.: Basic Topology, Volume 3: Algebraic Topology and Topology of Fiber Bundles. Springer, India (2022)
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Metadata
Title
Real-Valued Continuous Functions
Authors
Avishek Adhikari
Mahima Ranjan Adhikari
Copyright Year
2022
Publisher
Springer Nature Singapore
Book
Basic Topology 1

Print ISBN: 978-981-16-6508-0

Electronic ISBN: 978-981-16-6509-7

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-981-16-6509-7_6

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