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Derivatives

In: Elements of Mathematics Functions of a Real Variable

Author

Listed:
  • Elementary Theory
  • Philip Spain

    (University of Glasgow, Department of Mathematics)

Abstract

As was said in the Introduction, in this chapter and the next we shall study the infinitesimal properties of functions which are defined on a subset of the real field R and take their values in a Hausdorff topological vector space E over the field R; for brevity we shall say that such a function is a vector function of a real variable. The most important case is that where E = R (real-valued functions of a real variable). When E = R n , consideration of a vector function with values in E reduces to the simultaneous consideration of n finite real functions.

Suggested Citation

  • Elementary Theory & Philip Spain, 2004. "Derivatives," Springer Books, in: Elements of Mathematics Functions of a Real Variable, chapter 0, pages 3-49, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59315-4_2
    DOI: 10.1007/978-3-642-59315-4_2
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