5 · Find a quotient that points miss

A probe can support a continuous real-valued function that is not locally constant. Such a function gives information that the one-point probe cannot detect.

Try this. Set the variation to zero, then increase it and add finer stages. At zero, the map is locally constant. With variation, it keeps changing on smaller visible boxes.

Example 1.9 identifies the quotient as continuous functions modulo locally constant functions. This activity shows finite approximations to one nonzero class and does not prove that the pattern continues forever.