In this paper, we show that the correspondence discovered by Koshevoy ([18]) and Johnson and Dean ([15],[16]) between anti-exchange closure operators and path independent choice operators is a duality between two semilattices of such operators. Then we use this duality to obtain results...

In this paper, we show that the correspondence discovered by Koshevoy (1999) and, Johnson and Dean (1998) between anti-exchange closure operators and path independent choice operators is a duality between two semilattices of such operators. Then we use this duality to obtain old and new results...

We present a survey of properties of the lattice of closure systems (families of subsets of a set S containing S and closed by set intersection) on a finite set S with proofs of the more significant results. In particular, we prove that this lattice is atomistic and lower bounded and that there...