Covering - Mathematics

Mathematics

• In topology:
  • Covering map, a function from one space to another with uniform local neighborhoods
  • Cover (topology), a system of (usually, open or closed) sets whose union is a given topological space
  • Lebesgue covering dimension, a definition of dimension using topological properties
• In graph theory:
  • Vertex cover – a set of vertices incident on every edge
  • Edge cover – a set of edges incident on every vertex
  • Covering graph – a graph related to another graph via a covering map
  • cycle double cover, a family of cycles that includes every edge exactly twice
  • clique cover, a family of cliques that includes every vertex
  • path cover, a family of paths that includes every vertex
  • biclique cover, a family of complete bipartite graphs that includes every edge
• Covering lemma in set theory (specifically large cardinal theory)
• Covering number of a metric space, the minimum number of smaller balls needed to cover a unit ball
• Covering problems, computational tasks of finding a small family of sets whose union is a given set
• Covering set, in number theory, a set of prime numbers dividing all the elements of a sequence of numbers