  We show that immersed minimal surfaces of $\mathbb{R}^{3}$ with bounded
curvature and proper self intersections are proper. We also show that the
restriction of the immersing map to a wide component is always proper. When the
immersing map is injective the whole surface is a wide component. Prior to
these results it was only known that injectively immersed minimal surfaces with
bounded curvature were proper.

Differential Geometry;Metric Geometry