Abstract
The descriptive language of general topology is known to all mathematicians. The concept of a valuation allows one to introduce this language into the theory of algebraic numbers in a natural and fruitful way. We therefore propose to study some of the connections between valuation theory, algebraic number theory, and topology. Strictly speaking the topological considerations are just of a conceptual nature and in fact only the most elementary results on metric spaces and topological groups will be used; nevertheless these considerations are essential to the point of view taken throughout this chapter and indeed throughout the entire book.
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© 2000 Springer-Verlag Berlin Heidelberg
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O’Meara, O.T. (2000). Valuated Fields. In: Introduction to Quadratic Forms. Classics in Mathematics, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-62031-7_1
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DOI: https://doi.org/10.1007/978-3-642-62031-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66564-9
Online ISBN: 978-3-642-62031-7
eBook Packages: Springer Book Archive