Diameter of a Topological Manifold

Question

I know that for a Riemannian Manifold is defined the concept of diameter. I wuold know if it's defined a similar concept for a most general Topological Manifold.

Thanks in advance.

Answer 1

Riemannian manifold has a metric, which allows you to define lengths and distances.

A general topological manifold defines only the topology. Note that homeomorphisms do not preserve distances in general, so no concept of length and diameter can be defined for a topological manifold without additional structure.