<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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].</p></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].

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

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"The Space of Real Places on R(x,y)"}

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...

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

Published Online: Aug 24, 2018

Page range: 99 - 131

Received: Sep 08, 2016

Accepted: Dec 31, 2017

DOI: https://doi.org/10.1515/amsil-2017-0017

Keywords
real place, space of real places, strict system of polynomial extensions, Harrison set, path-connected, dense subset

© 2018 Ron Brown, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Aug 24, 2018

Page range: 99 - 131

Received: Sep 08, 2016

Accepted: Dec 31, 2017

DOI: https://doi.org/10.1515/amsil-2017-0017

Keywordsreal place, space of real places, strict system of polynomial extensions, Harrison set, path-connected, dense subset

© 2018 Ron Brown, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
real place, space of real places, strict system of polynomial extensions, Harrison set, path-connected, dense subset