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

2022 | OriginalPaper | Chapter

7. Countability, Separability and Embedding

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 special classes of topological spaces such as spaces satisfying either of the two axioms of countability formulated by Hausdorff in 1914 or satisfying the axiom of separability introduced by Frechét in 1906, both initiated in Chap. 3, which do not arise from the study of calculus and analysis in a natural way. They arise through a deep study of topology. The axiom of first countability arose through the study of convergent sequences.

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previous chapter Real-Valued Continuous Functions
next chapter Brief History of Topology I: Motivation of the Subject with Historical Development
Literature
Adhikari, M.R.: Basic Algebraic Topology and its Applications. Springer, India (2016) CrossRef
Adhikari, M.R.: Basic Topology, Volume 3: Algebraic Topology and Topology of Fiber Bundles. Springer, India (2022)
Adhikari, A., Adhikari, M.R.: Basic Topology, Volume 2: Topological Groups, Topology of Manifolds and Lie Groups. Springer, India (2022)
Adhikari, M.R., Adhikari, A.: Basic Modern Algebra with Applications. Springer, New Delhi, NewYork, Heidelberg (2014)
Borisovich, Y.C.U., Blznyakov, N., Formenko, T.: Introduction to Topology. Mir Publishers, Moscow (1985). Translated from the Russia by Oleg Efimov
Bredon, G.E.: Topology and Geometry. Springer-Verlag, New York (1983) MATH
Chatterjee, B.C., Ganguly, S., Adhikari, M.R.: Introduction to Topology. Asian Books, New Delhi (2002)
Kalajdzievski, K.: An Illustrated Introduction to Topology and Homotopy. CRC Press (2015)
Kelly, J.L.: General Topology, Van Nostrand, New York, 1955. Springer-Verlag, New York (1975)
Mendelson, B.: Introduction to Topology. College Mathematical Series. Allyn and Bacon, Boston (1962)
Stephen, W.: General Topology. Addison-Wesley (1970)
Metadata
Title
Countability, Separability and Embedding
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_7

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