DISLOCATED TOPOLOGIES
Pascal Hitzler – Anthony Karel Seda
We study a generalized notion of topology which evolved from 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. We show
that it is meaningful to discuss neighbourhoods, convergence, and
continuity in these spaces. A generalized version of the Banach contraction
mapping theorem can also be established. We will also show how the generalized
metrics studied here can be obtained from conventional metrics.
Keywords: generalized topology, generalized metric, generalized Banach
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