Expansiveness is a dynamical property: nearby points eventually separate. But “nearby” depends on the metric, and a metrizable space admits many compatible metrics. A system can be expansive with respect to one metric and not another. Metric-independent expansiveness asks for the strongest version: expansive with respect to every compatible metric.
The paper on metric-independent expansiveness (arXiv: 2603.20978) characterizes when this holds. For actions on locally compact spaces, metric-independent expansiveness is equivalent to a purely topological condition — cocompact expansivity — and also to the existence of an expansive extension to the one-point compactification.
The boundary of the compactification is the key. If the dynamics near infinity is “isolated” — if the point at infinity doesn't interact with the rest of the system — then expansiveness at finite scales lifts to the compactification, and the metric becomes irrelevant. The topological characterization strips away the metric entirely: what matters is the relationship between the dynamics and the space's ends.
The through-claim: a metric property becomes topological when the boundary is tame. Expansiveness depends on the metric only because the metric controls what happens at infinity. When the compactification boundary is dynamically isolated, all metrics agree, and the property becomes intrinsic. The metric is a choice; the topology is the constraint.
2603.20978. Dynamical systems / expansiveness / topological dynamics / compactification / metric independence.