An introduction to locally semialgebraic spaces
type: Item
instance of: scholarly article
title: An introduction to locally semialgebraic spaces
zbMATH Open document ID: 0586.14017
DOI: 10.1216/RMJ-1984-14-4-945
author: Hans Delfs
author: Manfred Knebusch
published in: Rocky Mountain Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Semi-algebraic geometry deals with subsets \(M\subset R^ n\) (R an arbitrary real closed field) which are boolean combinations of finitely many sets of the form \(\{x\in R^ n| \quad P(x)\geq 0\}\) where \(P\in R[X_ 1,...,X_ n]\). To study the geometry of such sets the authors introduced the category of semi-algebraic spaces over the real closed field R. However, certain questions cannot be treated satisfactorily in this setting. A case in point is the classification of coverings. This necessitates the introduction of a larger category, the category of locally semi-algebraic spaces. This paper contains the definition, examples and a few properties of these spaces. A full account of the theory of locally semi-algebraic spaces may be found in the authors' book [''Locally semi-algebraic spaces'', Lect. Notes Math. 1173 (1985; Zbl 0582.14006)].
reviewed by: Niels Schwartz
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 14E20
zbMATH DE Number: 3939500
zbMATH Keywords: real closed field
zbMATH Keywords: coverings
zbMATH Keywords: locally semi-algebraic spaces
MaRDI profile type: Publication
full work available at URL: rmj-1984-14-4-945
OpenAlex ID: W1990792920
description: scientific article; zbMATH DE number 3939500