Words fail me. The collapse of the material does not reduce the mass, it only concern grates it into a smaller volume. Now would that reduce the gravity ?
Even with a high school understanding of Newtonian gravity you should know that the gravitational force pulling the material inwards would increase (because it is getting closer to the centre, not because the mass is changing).
Assuming that the density is uniform the effect of increased gravitational force applies everywhere except the exact centre. To explain, the gravity cancels out at the centre because you'd have an equal force pulling in every direction. With a denser sphere of the same mass the component forces would be greater, but still cancel out. But if you move away from the centre the net force towards the centre would be stronger in the denser sphere, at any given distance from the centre.
quote: I may have missed some limitation on 'everywhere', but absent some limitation, your statement is wrong. It would violate Gauss' law.
Yes, you missed the context. We're only talking about the material that is collapsing and the forces operating it.
quote: No. Only for distances inside of the original surface of the sphere. I would further add, that most people would not be making a comparison to points inside of that original surface because those points are generally inaccessible.
Since the denser sphere is entirely contained within the original surface I defy you to find a point that is in the denser sphere, but that is not inside the original surface. I would also point out that in the case where we are talking about a gravitational collapse if is entirely sensible to talk about the gravitational force acting on the collapsing material.