|Publication Type||Journal Article|
|Year of Publication||2000|
|Authors||Pascal Hitzler, Anthony K. Seda|
|Keywords||Banach contraction, topologies|
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.
|Full Text|| |
Anthony K. Seda and Pascal Hitzler, 'Dislocated Topologies,' Department of Mathematics, University College Cork, Technical Report, 2000.