is a Boolean algebra and postfix <sup>I</sup> designates a unary operator, the interior operator, satisfying the identities:
x<sup>I</sup> ≤ x
x<sup>II</sup> = x<sup>I</sup>
(xy)<sup>I</sup> = x<sup>I</sup>y<sup>I</sup>
1<sup>I</sup> = 1
x<sup>I</sup> is called the interior of x.
The dual of the interior operator is the closure operator <sup>C</sup> defined by x<sup>C</sup> = ((x ' )<sup>I</sup> )'. x<sup>C</sup> is called the closure of x. By the principle of duality, the closure operator satisfies the identities: