Schröder–Bernstein property

A Schröder–Bernstein property is any mathematical property that matches the following pattern: If, for some mathematical objects X and Y, both X is similar to a part of Y and Y is similar to a part of X, then X and Y are similar (to each other). The name Schröder–Bernstein (or Cantor–Schröder–Bernstein, or Cantor–Bernstein) property is in analogy to the theorem of the same name (from set theory).