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Separation Axioms

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Basic Topology 1

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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References

  • Adhikari, M.R.: Basic Algebraic Topology and its Applications. Springer, India (2016)

    Book  Google Scholar 

  • Adhikari, M.R.: Basic Topology, Volume 3: Algebraic Topology and Topology of Fiber Bundles. Springer, India (2022)

    Google Scholar 

  • Adhikari, M.R., Adhikari, A.: Basic Modern Algebra with Applications. Springer, New Delhi, New York, Heidelberg (2014)

    Book  Google Scholar 

  • Adhikari, A., Adhikari, M.R.: Basic Topology, Volume 2: Topological Groups, Topology of Manifolds and Lie Groups. Springer, India (2022)

    Google Scholar 

  • Bredon, G.E.: Topology and Geometry. Springer-Verlag, New York (1983)

    MATH  Google Scholar 

  • Borisovich, Y.C.U., Blznyakov, N., Formenko, T.: Introduction to Topology. Mir Publishers, Moscow (1985). Translated from the Russia by Oleg Efimov

    Google Scholar 

  • Brown, R.: Topology: A Geometric Account of General Topology, Homotopy Types, and the Fundamental Groupoid. Wiley, New York (1988)

    MATH  Google Scholar 

  • Chatterjee, B.C., Ganguly, S., Adhikari, M.R.: Introduction to Topology. Asian Books, New Delhi (2002)

    Google Scholar 

  • Conway, J.B.: A Course in Point Set Topology. Springer, Switzerland (2014)

    Book  Google Scholar 

  • Dugundji, J.: Topology. Allyn & Bacon, Newton, MA (1966)

    MATH  Google Scholar 

  • Fuks, D.B., Rokhlin, V.A.: Beginner’s Course in Topology. Springer-Verlag, New York (1984)

    Book  Google Scholar 

  • Hu, S.T.: Introduction to General Topology. Holden-Day, San Francisco (1966)

    MATH  Google Scholar 

  • Kelly, J.L.: General Topology, Van Nostrand, New York, 1955. Springer-Verlag, New York (1975)

    Google Scholar 

  • Munkres, J.R.: Topology. Prentice-Hall, New Jersey (2000)

    MATH  Google Scholar 

  • Patterson, E.M.: Topology. Oliver and Boyd (1959)

    Google Scholar 

  • Singer, I.M., Thorpe, J.A.: Lecture Notes on Elementary Topology and Geometry. Springer-Verlag, New York (1967)

    MATH  Google Scholar 

  • Stephen, W.: General Topology. Addison-Wesley (1970)

    Google Scholar 

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Correspondence to Avishek Adhikari .

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Adhikari, A., Adhikari, M.R. (2022). Separation Axioms. In: Basic Topology 1. Springer, Singapore. https://doi.org/10.1007/978-981-16-6509-7_4

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