Cactoid

A locally connected continuum $C$ that is the closure of the sum of at most a countable number of spheres $S-i$ and simple arcs $D_i$ located in Euclidean space $\mathbf{E}^3$, and such that for each closed contour $L \subset C$ there exists exactly one sphere $S_i$ containing it. Cactoids, and they alone, are monotone images of the $2$-dimensional sphere $S^2$; also, every cactoid is a monotone open image of $S^2$.