Aligned spaces generalize topological spaces and generate Higgs spaces. We give a necessary and sufficient condition for a finite aligned space to be a topological space, we prove the existence of two kinds of convex ...Aligned spaces generalize topological spaces and generate Higgs spaces. We give a necessary and sufficient condition for a finite aligned space to be a topological space, we prove the existence of two kinds of convex geometries, and we compare several concepts and results for arbitrary (that is, not necessarily finite) aligned, topological and Higgs spaces.展开更多
文摘Aligned spaces generalize topological spaces and generate Higgs spaces. We give a necessary and sufficient condition for a finite aligned space to be a topological space, we prove the existence of two kinds of convex geometries, and we compare several concepts and results for arbitrary (that is, not necessarily finite) aligned, topological and Higgs spaces.