Point-finite collection

In mathematics, a collection or family ${\displaystyle {\mathcal {U}}}$ of subsets of a topological space ${\displaystyle X}$ is said to be point-finite if every point of ${\displaystyle X}$ lies in only finitely many members of ${\displaystyle {\mathcal {U}}.}$^[1][2]

A

of subsets of a topological space is also point-finite. A topological space in which every open cover admits a locally finite open refinement is called a paracompact space. Every paracompact space is therefore metacompact.^[2]

References

• Willard, Stephen (2004) [1970]. General Topology.
  OCLC 115240
  .
• Willard, Stephen (2012) [1970]. General Topology.
  OCLC 829161886
  .

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