Topological groups, which integrate algebraic group structures with continuous topologies, and metric spaces, defined by a distance function, form a fundamental basis for modern mathematical analysis.

We prove two theorems concerning Lyapunov functions on metric spaces. The new element in these theorems is the lack of a hypothesis of compactness or local compactness. The first theorem applies to a ...

We prove a compactness theorem for the dual Gromov-Hausdorff propinquity as a noncommutative analogue of the Gromov compactness theorem for the Gromov-Hausdorff distance. Our theorem is valid for ...