On the geometry of physical measurements: Topological and algebraic aspects

We study the mathematical structure of notion measurement space, which extends aspects noncommutative topology that are based on quantale theory. This yields a geometric model physical measurements provides realist picture, yet also operational, such and classical information arise interdependently as primitive concepts. A derived observer caters for formulation Bohr's classical/quantum divide. Two important classes spaces obtained, respectively from C*-algebras second-countable locally compact open sober topological groupoids. The latter yield type relate to Schwinger's selective measurement. show space associated reduced C*-algebra any Hausdorff étale groupoid is canonically equipped with observer, we establish correspondence between properties groupoid.