The space of real places on ℝ(x, y)
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].
Keywords
real place; space of real places; strict system of polynomial extensions; Harrison set; path-connected; dense subset
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Department of Mathematics, Univeristy of Hawaii, USA United States
Department of Mathematics, Soka University of America, USA United States
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