If topology is called rubber-sheet geometry, would it be accurate to describe the "cut and shuffle" topic of "piecewise isometries" as broken glass geometry ?
Isometry sounds more geometrical than topological. What would be a good name for "piecewise topology" ? If you take a topological space and break it up and put it back together in a random way, not necessarily in one piece, then what could you say about the topology of the resulting jumble ?