Dislocated Topologies
Document Type
Article
Publication Date
5-2-2000
Abstract
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 requirement that a neighbourhood of a point includes the point itself, and by allowing neighbourhoods of points to be empty. The corresponding 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 neighbourhoods, convergence, and continuity in these spaces. A generalized version of the Banach contracting mapping theorem can also be established. We show finally how the generalized metrics studied here can be obtained from conventional metrics.
Repository Citation
Hitzler, P.,
& Seda, A. K.
(2000). Dislocated Topologies. .
https://corescholar.libraries.wright.edu/cse/15
