Möbius Strips Defy a Link with Infinity

Think about how you could fill a 2D plane with infinite parallel lines, one for every single point on a real line. Imagine, for example, running vertical lines through every point on the x-axis, how this would fill the entire plane.

The Hopf Fibration is similar. It's a way of filling all of the space on the surface of a 3-sphere (which locally feels like 3D Euclidean space) with interlocking circles. Each of these circles can be mapped a point on an ordinary sphere.

Thinking of it in the other direction: for every point on the surface of an ordinary (2-)sphere, you can assign a circle on the surface of a 3-sphere. By taking into consideration all of the points on the 2-sphere, and all of the circles they represent, you can fill the entire surface of the 3-sphere with these interlocking circles!