Integer broom topology

[1] The integer broom space X is a subset of the plane R2.

Assume that the plane is parametrised by polar coordinates.

[1] The image on the right gives an illustration for 0 ≤ n ≤ 5 and 1/15 ≤ θ ≤ 1.

Geometrically, the space consists of a collection of convergent sequences.

The integer broom space is given by the polar coordinates Let us write (n,θ) ∈ U × V for simplicity.