• P. V. SubrahmanyamEmail author
Part of the Forum for Interdisciplinary Mathematics book series (FFIM)


This chapter is a precis of the basic definitions and theorems used in the sequel. It is presumed that the reader is familiar with naive set theory (see Halmos [4]) and the properties of real numbers and real functions (see Bartle [1]). Other mathematical concepts and theorems relevant to specific sections of a chapter will be recalled therein.


  1. 1.
    Bartle, R.G.: The Elements of Real Analysis, 2nd edn. Wiley, New York (1976)Google Scholar
  2. 2.
    Bollobas, B.: Linear Analysis, An Introductory Course, 2nd edn. Cambridge University Press, Cambridge (1999)Google Scholar
  3. 3.
    Dugundji, J.: Topology. Allyn and Bacon Inc., Boston (1966)Google Scholar
  4. 4.
    Halmos, P.R.: Naive Set Theory. D. Van Nostrand Co., Princeton (1960)Google Scholar
  5. 5.
    Kantorovich, L.V., Akilov, G.P.: Functional Analysis, Translated from the Russian by Howard L. Silcock, 2nd edn. Pergamon Press, Oxford-Elmsford (1982)CrossRefGoogle Scholar
  6. 6.
    Kaplansky, I.: Set Theory and Metric Spaces, 2nd edn. Chelsea Publishing Co., New York (1977)Google Scholar
  7. 7.
    Kelley, J.L.: General Topology. D. Van Nostrand Company, Inc., Toronto (1955)Google Scholar
  8. 8.
    Lusternik, L.A., Sobolev, V.J.: Elements of Functional Analysis. Hindustan Publishing Corporation, Delhi (1974)zbMATHGoogle Scholar
  9. 9.
    Munkres, J.R.: Topology: A First Course. Prentice-Hall, Inc., Englewood Cliffs (1975)zbMATHGoogle Scholar
  10. 10.
    Royden, H.L.: Real Analysis, 3rd edn. Macmillan Publishing Company, New York (1988)Google Scholar
  11. 11.
    Rudin, W.: Functional Analysis. Tata McGraw-Hill Publishing Co. Ltd., New Delhi (1974)Google Scholar
  12. 12.
    Rudin, W.: Real and Complex Analysis, 3rd edn. McGraw-Hill Book Co., New York (1987)Google Scholar
  13. 13.
    Simmons, G.F.: Introduction to Topology and Modern Analysis. McGraw-Hill Book Co., Inc., New York (1963)Google Scholar
  14. 14.
    Taylor, A.E.: Introduction to Functional Analysis. Wiley, New York; Chapman Hall, Ltd., London (1958)Google Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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