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Not quite. If by "edge" you mean the surface of the earth, then the force of gravity from the closer edge will always exactly offset the gravity from the farther edge. So if the earth were hollow, then you would experience zero gravity at any point in the hollow portion.
Of course, the earth is not hollow. And any mass under you (i.e. closer to the center than you are) will not be offset, and all of it will pull you towards the center. As you move further away from the center, more of the earth's mass will be closer to the center than you and therefore the force of gravity will increase.
Excellent point, well made!
So if the original poster wanted to have a 10km sphere in the center of the earth of zero gravity (earth gravity at least), then all they have to do is hollow out 10km and they are good to go?
Nah, there's only one exact center of gravity for a given body of mass. You can't just make a vacuum and have gravity equalizer throughout it.
Yes you can, as long as you are inside a perfectly spherical shell.
From: http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/sphshell2.html#wtls