Abstract
This is the first of four chapters in which we look at various aspects of Riemann’s work and the way it changed the theory of real and complex functions.
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Notes
- 1.
In modern terms, a set A is nowhere dense in another set B if the closure of the interior of A is empty. We shall see that this concept was not reliably understood in the period before it was made precise by the techniques of 20th century topology.
- 2.
For a biography of Riemann, see Laugwitz, Bernhard Riemann (2000).
- 3.
See Pulte in Jacobi (1996).
- 4.
The entire paper has been translated into English and published in Bernhard Riemann, Collected papers, translated by Roger Baker, Charles Christenson and Henry Orde, Kendrick Press, 2004; see pp. 219–256.
- 5.
Riemann’s notation for this function was (x), but this causes problems by disappearing when the function is composed with others, so I have introduced this notation.
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Gray, J. (2015). Riemann. In: The Real and the Complex: A History of Analysis in the 19th Century. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-23715-2_15
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DOI: https://doi.org/10.1007/978-3-319-23715-2_15
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