Published: 2018-01-31

The space of real places on ℝ(x, y)

Ron Brown , Jonathan L. Merzel

Abstract

The space M(ℝ(x, y)) of real places on ℝ(x, y) is shown to be path-connected. The possible value groups of these real places are determined and for each one it is shown that the set of real places with that value group is dense in the space. Large collections of subspaces of the space M(ℝ(x, y)) are constructed such that any two members of such a collection are homeomorphic. A key tool is a homeomorphism between the space of real places on ℝ((x))(y) and a certain space of sequences related to the “signatures” of [2], which themselves are shown here to be related to the “strict systems of polynomial extensions” of [3].

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Brown, R., & Merzel, J. L. (2018). The space of real places on ℝ(x, y). Annales Mathematicae Silesianae, 32, 99–131. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13916

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Domyślna okładka

Vol. 32 (2018)
Published: 2018-08-24


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

Licence CC Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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