Thursday, June 4, 2009
Ken's mention of Menger Sponges brought up the association with the Cantor set and the Sierpinski triangle. There must be a name for a topological property of objects from which a congruent copy/s of itself can be removed and the remaining portions of the object are equivalent to the removed piece. The interval, cube, and triangle are all such objects. It seems to me that there is now way that the circle is. Togologists help!