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The Space of Sections as a Topological Space

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Rational Points and Arithmetic of Fundamental Groups

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2054))

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Abstract

In this chapter we shall shift our focus from an individual section to the space of all sections at once. The space of sections naturally forms a pro-discrete topological space, see Lemma 44, which allows important limit arguments in arithmetically relevant cases, see Lemma 48. The fundamental notion of a neighbourhood of a section is introduced and used to describe the decomposition tower of a section.

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References

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Authors and Affiliations

  1. Mathematics Center Heidelberg (MATCH), University of Heidelberg, Heidelberg, Germany

    Jakob Stix

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  1. Jakob Stix
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Stix, J. (2013). The Space of Sections as a Topological Space. In: Rational Points and Arithmetic of Fundamental Groups. Lecture Notes in Mathematics, vol 2054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30674-7_4

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