Some properties of cyclic flats of an infinite matroid

We prove that when a pre-independence space satisfies some natural properties, then its cyclic flats form a bounded lattice under set inclusion. Additionally, we show that a bounded lattice is isomorphic to the lattice of cyclic flats of a pre-independence space. We also prove that the notion of cyclic width gives rise to dual-closed and minor-closed classes of B-matroids. Finally, we find a difference between finite matroids and B-matroids by using the notion of well-quasi-ordering.