01062nas a2200133 4500008004100000245002600041210002600067520071500093653002300808653001500831100002000846700002200866856004000888 2000 eng d00aDislocated Topologies0 aDislocated Topologies3 aWe study a generalized notion of topology which evolved out of applications in the area of logic programming semantics. The generalization is obtained by relaxing the requirements that a neighbourhood of a point includes the point itself, and by allowing neighbourhoods of points to be empty. The correspoding generalized notion of metric is obtained by allowing points to have non-zero distance to themselves. We further show that it is meaningful to discuss neightbourhoods, convergence, and continuity in these spaces. A generalized version of the Banach contraction mapping theorem can also be established. We show finally how the generalized metrics studied here can be obtained from conventional metrics.10aBanach contraction10atopologies1 aHitzler, Pascal1 aSeda, Anthony, K. uhttp://knoesis.wright.edu/node/1630