TY - JOUR
T1 - Dislocated Topologies
Y1 - 2000
A1 - Pascal Hitzler
A1 - Anthony K. Seda
KW - Banach contraction
KW - topologies
AB - We 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.
ER -