Note that this embedding depends on the chosen point x and is therefore not entirely canonical.

Again, manifold means that locally at any point x of X, the space is supposed to be like the real plane.

Here the point x' is assumed to be in the domain of (the natural extension of) f.

(iii) The point x lies in the closure of Y.

Now, we must continue the differential operator to the central point x in the punctured neighborhood.

Because the potential U defines a force F at every point x in space, the set of forces is called a force field.

Assume first that some initial feasible point x is given.

Therefore there is a point x in this intersection.

In fact the map taking A to a point x is not universally closed.

Some were even supposed to have reached point 'X' for the rendezvous with the 46th Division.