[gaouirog] Topology of dimensions

A 2D plane through 3D space divides the set of all 0D points in space into two classes: those on either side of the plane.  (Ignoring the plane itself).

A 1D line through space divides all possible 1D closed loops through space into two classes: those which loop around the line (knotted as in knot theory) and those which do not. One can loop around multiple times, clockwise or counterclockwise.

A 0D point in space divides all possible closed 2D surfaces in space into two classes: those which enclose the point and those which do not.

The sum of the dimensions is one less than dimension of the space.

2D version: points and loops, lines and points.

The game of sprouts, and its 3D analogue.