The space of real places on ℝ(x, y)
Journal Title: Annales Mathematicae Silesianae - Year 2018, Vol 32, Issue
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].
Authors and Affiliations
Ron Brown, Jonathan L. Merzel
Keywords
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