The structure of spaces of \(\mathbb{R}\)-places of rational function fields over real closed fields

DOI10.1216/RMJ-2016-46-2-533zbMath1380.12009MaRDI QIDQ309477

Katarzyna Kuhlmann

Publication date: 7 September 2016

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1469537476

zbMATH Keywords

covering dimensionvaluationssmall inductive dimensionmetrizableultrametricBaer-Krull theoremfractal structuresfunction families that separate pointsgeneralized Dedekind cutsHarrison topologylarge inductive dimensionspaces of places

Mathematics Subject Classification ID

Compact (locally compact) metric spaces (54E45) Dimension theory in general topology (54F45) Non-Archimedean valued fields (12J25) Ordered fields (12J15) Real algebra (13J30) General valuation theory for fields (12J20)

Related Items (6)

The space of \(\mathbb{R}\)-places on a rational function field ⋮ Topology of spaces of valuations and geometry of singularities ⋮ On the dimension of the space of \(\mathbb R\)-places of certain rational function fields ⋮ The space of real places on \(\mathbb{R}(x; y)\) ⋮ Selected methods for the classification of cuts, and their applications ⋮ Weakly contractive iterated function systems and beyond: a manual

Cites Work

• Unnamed Item
• On the rim-structure of continuous images of ordered compacta
• On self-homeomorphic spaces
• Embedding ordered fields in formal power series fields
• On the dimension of the space of \(\mathbb R\)-places of certain rational function fields
• Embedding theorems for spaces of R-places of rational function fields and their products
• Metrizability of Spaces of ℝ-places of Function Fields of Transcendence Degree 1 Over Real Closed Fields
• Chains of higher level orderings
• Valued Fields

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