  The emergence of an autocatalytic network from an available set of elements
is a fundamental step in early evolutionary processes, such as the origin of
metabolism. Given a set of elements, the reactions between them (chemical or
otherwise), and certain elements catalysing certain reactions, a Reflexively
Autocatalytic F-generated (RAF) set is a subset $R'$ of reactions that is
self-generating from a given food set, and with each reaction in $R'$ being
catalysed from within $R'$. RAF theory has been applied to various phenomena in
theoretical biology, and a key feature of the approach is that it is possible
to efficiently identify and classify RAFs within large systems. This is
possible because RAFs can be described as the (nonempty) subsets of the
reactions that are the fixed points of an (efficiently computable) interior map
that operates on subsets of reactions. Although the main generic results
concerning RAFs can be derived using just this property, we show that for
systems with at least 12 reactions there are generic results concerning RAFs
that cannot be proven using the interior operator property alone.
