Preclosure operator

In topology, a preclosure operator, or Čech closure operator is a map between subsets of a set, similar to a topological closure operator, except that it is not required to be idempotent. That is, a preclosure operator obeys only three of the four Kuratowski closure axioms.

A preclosure operator on a set ${\displaystyle X}$ is a map ${\displaystyle [\quad ]_{p}}$

where ${\displaystyle {\mathcal {P}}(X)}$ is the power set of ${\displaystyle X}$.

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