Lets assume i start bending space from one point into other like the way we do it on paper. Since space has no length or width we can do it. On paper will be different and paper will be turned into infinite long "stick". Let me draw it for you.
If we bend it only once do we get to pull off all planets in the direction we are pulling or they stay on same place? ... and we do that infinite times... Did we broke the space? What will happen with the planets around that hole?