Stand-up Maths on youtube recently asserted that, at least to topologists, a torus is a hollow rather than a solid donut. Is that something particular to topological domains or is the title on this incorrect?
You can say exactly the same thing for a sphere. Really a sphere is just the skin, but in practice people will use phrases like "within the sphere" etc.. So it really doesn't matter, when it does people refer to the "boundary" of it or will just write some equations.
Topologically the hollow torus is more interesting, the solid one is effectively a slightly thicker circle.
I was very confused until I realized you meant the boundary of a circle, not a filled circle.
A filled circle is called a disk (or 2-ball) in math.