MINIMALITY WITH RESPECT TO YOUNGS AXIOM

A topological space (X, tau) satisfies Youngs axiom (or is T-Y) if and only if given distinct elements x, y in X, {(x) over bar} boolean AND {(y) over bar} has cardinality at most one. Accordingly, given the lattice of all topologies definable for an infinite set X, those which are minimal with respect to T-Y are identified. The approach adopted develops a technique which exploits the dual order-topological nature of any given space. Thus, an alternative description of the topologically-established minimal structure in terms of the behaviour of the naturally-occurring specialisation order and the intrinsic topology on the resulting partially ordered set is offered.