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Introduction to Continuity

In: From Calculus to Analysis

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  • Steen Pedersen

    (Wright State University, Department of Mathematics)

Abstract

In this chapter the algebra of continuous functions is established. A function that is continuous at each irrational number and discontinuous at each rational number is constructed. This function is know as the Riemann function, the Thomae function, the ruler function, or the raindrop function.

Suggested Citation

  • Steen Pedersen, 2015. "Introduction to Continuity," Springer Books, in: From Calculus to Analysis, edition 127, chapter 2, pages 45-50, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13641-7_2
    DOI: 10.1007/978-3-319-13641-7_2
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