Dislocated Topologies

TitleDislocated Topologies
Publication TypeJournal Article
Year of Publication2000
AuthorsPascal Hitzler, Anthony K. Seda
KeywordsBanach contraction, topologies
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 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.

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