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# TDB

Next, we can look at the composite functions:

$g \circ f: 2^X \rightarrow 2^X$ $f \circ g: 2^Y \rightarrow 2^Y$

Given that $$f$$ and $$g$$ form a Galois connection, it follows that these composites are closure operators.
• Monotone: $$a \subseteq b \implies T(a) \subseteq T(b)$$
Comment Source:Given that \$$f\$$ and \$$g\$$ form a Galois connection, it follows that these composites are **closure operators**. For a function T mapping a partially ordered set into itself, this means that T is: * Monotone: \$$a \subseteq b \implies T(a) \subseteq T(b)\$$ *