Metric Spaces

  • Anthony N. Michel
  • Charles J. Herget

Abstract

Up to this point in our development we have concerned ourselves primarily with algebraic structure of mathematical systems. In the present chapter we focus our attention on topological structure. In doing so, we introduce the concepts of “distance” and “closeness.” In the final two chapters we will consider mathematical systems endowed with algebraic as well as topological structure.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [5.1]
    E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations. New York: McGraw-Hill Book Company, Inc., 1955.MATHGoogle Scholar
  2. [5.2]
    E. T. Copson, Metric Spaces. Cambridge, England: Cambridge University Press, 1968.MATHGoogle Scholar
  3. [5.3]
    A. M. Gleason, Fundamentals of Abstract Analysis. Reading, Mass.: Addison-Wesley Publishing Co., Inc., 1966.MATHGoogle Scholar
  4. [5.4]
    M. E. Goldstein and B. M. Rosenbaum, “Introduction to Abstract Analysis,” National Aeronautics and Space Administration, Report No. SP-203, Washington, D.C., 1969.Google Scholar
  5. [5.5]
    L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces. New York: The Macmillan Company, 1964.MATHGoogle Scholar
  6. [5.6]
    J. Kelley, General Topology. Princeton, N.J.: D. Van Nostrand Company, Inc., 1955.MATHGoogle Scholar
  7. [5.7]
    A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis. Vol. 1. Albany, N.Y.: Graylock Press, 1957.Google Scholar
  8. [5.8]
    A. W. Naylor and G. R. Sell, Linear Operator Theory in Engineering and Science. New York: Holt, Rinehart and Winston, 1971.Google Scholar
  9. [5.9]
    H. L. Royden, Real Analysis. New York: The Macmillan Company, 1965.Google Scholar
  10. [5.10]
    A.E. Taylor, General Theory of Functions and Integration. New York: Blaisdell Publishing Company, 1965.MATHGoogle Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Anthony N. Michel
    • 1
  • Charles J. Herget
    • 2
  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.Herget AssociatesAlamedaUSA

Personalised recommendations