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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adhikari, M.R.: Basic Algebraic Topology and its Applications. Springer, India (2016)
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)
Chatterjee, B.C., Ganguly, S., Adhikari, M.R.: Introduction to Topology. Asian Books, New Delhi (2002)
Dugundji, J.: Topology. Allyn & Bacon, Newton, MA (1966)
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)
Morris, S.A.: Topology without tears. http://www.econphd.net/notes.htm (2007)
Munkres, J.R.: Topology. Prentice-Hall, New Jersey (2000)
Stephen, W.: General Topology. Addison-Wesley (1970)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Adhikari, A., Adhikari, M.R. (2022). Countability, Separability and Embedding. In: Basic Topology 1. Springer, Singapore. https://doi.org/10.1007/978-981-16-6509-7_7
Download citation
DOI: https://doi.org/10.1007/978-981-16-6509-7_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-6508-0
Online ISBN: 978-981-16-6509-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)