Definitions of correspondence:

• noun:   communication by exchange of letters
• noun:   communication by the exchange of letters
• noun:   compatibility of observations

  Example: "The results of two tests were in correspondence"

• noun:   similarity by virtue of correspondence
• noun:   the relation of correspondence in degree or size or amount
• noun:   (mathematics) an attribute of a shape or relation; exact correspondence of form on opposite sides of a dividing line or plane
• noun:   a function such that for every element of one set there is a unique element of another set