I really struggled to remember this definition.

Eventually, I hit upon this idea: a set of subsets is locally finite if every point in the space is close to only finitely many of those sets, where close means "has a neighborhood intersecting".

I really struggled to remember this definition.

Eventually, I hit upon this idea: a set of subsets is locally finite if every point in the space is close to only finitely many of those sets, where close means "has a neighborhood intersecting".