Automated reasoning about elementary point-set topology (Q1122363)

The authors use a first-order formulation of point set topology using sorted logic where one has three types of objects: viz., points, sets of points and collections of sets of points. The use of typed variables, however, presents difficulties when one applies automated reasoning. The authors try to get around this difficulty by using ``implicit typing'' where the position of an argument determines its type. Using this formal framework the authors describe the basic notions of point set topology and they give a resolution proof of the fact that a basis generates a topology with that basis.