Algebraic classification of physical structures with zero. II. Topological aspects

Some topological analogs are obtained of the author’s previous results on the classification of physical structures. A topological-algebraic axiomatics is considered enabling us to replace the algebraic axiom corresponding to the main equation of a physical structure by a more natural axiom. A physical structure of rank different from (2, 2) is shown to be a pair of vector spaces with a nondegenerate bilinear form over a topological skew field. The obtained results are applied to the classification of physical structures of rank different from (2, 2). The structures of rank (2, 2) are also considered. To describe them, a topological group structure corresponding to the biform action is introduced on the set of measurements.