Definition:Inflationary Mapping/Subset

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Let $C$ be a class.

Let $f: C \to C$ be a mapping from $C$ to $C$.

Then $f$ is inflationary if and only if:

$x \in C \implies x \subseteq \map f x$

That is, if and only if for each $x \in C$, $x$ is a subset of $\map f x$.

Also known as

An inflationary mapping is also known as a progressive mapping or progressing mapping.

Some sources use progressing function.

Also see

  • Results about inflationary mappings can be found here.