Refinement
A refinement X of a cover Y is a cover such that every element x in X is a subset of an element y in Y.
See also
CoverExplore with Wolfram|Alpha
WolframAlpha
Cite this as:
Weisstein, Eric W. "Refinement." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Refinement.html