A relative notion of local completeness in semialgebraic geometry (Q1812813)

This paper introduces the concept of a locally proper map between locally semialgebraic spaces over a real closed field. Local properness can be regarded as the generalization to maps of the notion of local completeness. The authors use this to give an easy semialgebraic proof that a proper map between semialgebraic spaces is affine. They study the notion of locally proper map further, giving a characterization in terms of the induced map on real closed spaces.