Separation, retractions and homotopy extension in semialgebraic spaces

Hans Delfs and Manfred Knebusch

Vol. 114 (1984), No. 1, 47–71

DOI: 10.2140/pjm.1984.114.47

Abstract

We consider an affine semialgebraic space M over a real closed field R. Tietze’s extension theorem holds in M. Every closed semialgebraic subset A of M is a strong deformation retract of a semialgebraic neighbourhood Z in M, and (M,A) has the homotopy extension property. If A is locally complete then Z can be chosen as a mapping cylinder.

Mathematical Subject Classification 2000

Primary: 14G30, 14G30

Secondary: 11E10, 12D15, 14F35, 57P05, 57Q99

Milestones

Received: 2 August 1982

Published: 1 September 1984