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

2022 | OriginalPaper | Chapter

4. Separation Axioms

Authors : Avishek Adhikari, Mahima Ranjan Adhikari

Published in: Basic Topology 1

Publisher: Springer Nature Singapore

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Abstract

This chapter studies topological spaces by imposing certain conditions, called separation axioms on these spaces in terms of their points and open sets, specially, where there is possibly no concept of distance. The additional conditions are needed, because the defining axioms for a topological space are extremely general and they are too weak to study them in depth.

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previous chapter Topological Spaces and Continuous Maps
next chapter Compactness and Connectedness
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, M.R., Adhikari, A.: Basic Modern Algebra with Applications. Springer, New Delhi, New York, Heidelberg (2014) CrossRef
Adhikari, A., Adhikari, M.R.: Basic Topology, Volume 2: Topological Groups, Topology of Manifolds and Lie Groups. Springer, India (2022)
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Chatterjee, B.C., Ganguly, S., Adhikari, M.R.: Introduction to Topology. Asian Books, New Delhi (2002)
Conway, J.B.: A Course in Point Set Topology. Springer, Switzerland (2014) CrossRef
Fuks, D.B., Rokhlin, V.A.: Beginner’s Course in Topology. Springer-Verlag, New York (1984) CrossRef
Hu, S.T.: Introduction to General Topology. Holden-Day, San Francisco (1966) MATH
Kelly, J.L.: General Topology, Van Nostrand, New York, 1955. Springer-Verlag, New York (1975)
Patterson, E.M.: Topology. Oliver and Boyd (1959)
Singer, I.M., Thorpe, J.A.: Lecture Notes on Elementary Topology and Geometry. Springer-Verlag, New York (1967) MATH
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Metadata
Title
Separation Axioms
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_4

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