Convergence-theoretic approach to quotient quest

Several classes of quotient maps are characterized in terms of projections on certain convergence classes. Various classes of topologies are characterized in terms of quotient types of the identity map with respect to certain convergence modifications of topologies. General preservation and representation theorems are presented; they recover numerous classical theorems. On the other hand, recent results on topological maximality within convergence classes enable one to deduce that a map is of some quotient class from the corresponding maximality of the range topology; thus classical results on accessibilty and strong accessibility are recovered.