  This work proposes an alternative approach to the so-called lattice of
embedded subsets, which is included in the product of the subset and partition
lattices of a finite set, and whose elements are pairs consisting of a subset
and a partition where the former is a block of the latter. The lattice
structure proposed in a recent contribution relies on ad-hoc definitions of
both the join operator and the bottom element, while also including
join-irreducible elements distinct from atoms. Conversely, here embedded
subsets obtain through a closure operator defined over the product of the
subset and partition lattices, where elements are generic pairs of a subset and
a partition. Those such pairs that coincide with their closure are precisely
embedded subsets, and since the Steinitz exchange axiom is also satisfied, what
results is a geometric (hence atomic) lattice given by a simple matroid (or
combinatorial geometry) included in the product of the subset and partition
lattices (as the partition lattice itself is the polygon matroid defined on the
edges of a complete graph). By focusing on its M\"obius function, this
geometric lattice of embedded subsets of a n-set is shown to be isomorphic to
the lattice of partitions of a n+1-set.
