Open locally semi-algebraic maps

Niels Schwartz
1988 Journal of Pure and Applied Algebra  
In semi-algebraic geometry examples of open morphisms occur naturally, for example coverings. This paper emphasizes the investigation of open morphisms of locally semi-algebraic spaces from the point of view of real closed spaces. This means that real spectra and algebraic properties of rings of sections of locally semi-algebraic spaces play a role. Typical examples for results coming up in this context are the following: Open morphisms can be characterized in terms of a lifting property of
more » ... ialization chains in real spectra. For morphisms into semi-algebraic paths, openness and flatness are equivalent conditions. Rg------+R c n cn " B-C commutes (where we identify Ii" Rc with the fields of representatives). We can write B=R,i-m" C= R,tm,.
doi:10.1016/0022-4049(88)90017-5 fatcat:eowcwojdg5e5tl4y7wmldwmenq