adj. (of a region of the complex plane) having no holes in it, so that its complement in the extended plane is also connected. For example a circle is simply connected but an annulus is not, since its complement consists of two unconnected regions. More generally, connectivity of a surface is defined in terms of the Euler characteristic for the surface. A region in three-space is simply connected if every simple closed curve in the region bounds a surface of which the graph is in the region. This fails for the interior of the torus but holds for the sphere.