The Space of Real Places on R(x,y)

• Main Authors: Brown Ron, Merzel Jonathan L.
• Format: Article
• Language: English
• Published: Sciendo 2018-09-01
• Series: Annales Mathematicae Silesianae
• Subjects: real place; space of real places; strict system of polynomial extensions; Harrison set; path-connected; dense subset
• Online Access: http://www.degruyter.com/view/j/amsil.2018.32.issue-1/amsil-2017-0017/amsil-2017-0017.xml?format=INT

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].