1) General question : Let's take a usual line : it's a 1D manifold in 2D space. The line is closed if there are no border points. (circle, aso...) Let suppose a usual surface : it's a 2D manifold enbedded in 3D space. The surface is closed if there are no border line. (sphere, torus, aso...) Let's suppose a 3D manifold embedded in 4D space. The manifold (volume) is closed if there are no border surface ??? How can one represent a closed volume which is not infinite ?? The usual Ball (with it's interior) is not closed, because there is a border surface (the outer sphere). Neither a torus, neither any 3D shape I could imagine. 2) Precise question : Let's assume a 4D manifold is given by F(w,x,y,z)=0, such that w=w(r,s,t), aso for x,y,z.... Question : How do I know the described manifold is closed ? Any reference ? BTW : I ask this question in relation with the Poincare Conjecture.