331 research outputs found
Lawson topology of the space of formal balls and the hyperbolic topology
AbstractLet (X,d) be a metric space and BX=X×R denote the partially ordered set of (generalized) formal balls in X. We investigate the topological structures of BX, in particular the relations between the Lawson topology and the product topology. We show that the Lawson topology coincides with the product topology if (X,d) is a totally bounded metric space, and show examples of spaces for which the two topologies do not coincide in the spaces of their formal balls. Then, we introduce a hyperbolic topology, which is a topology defined on a metric space other than the metric topology. We show that the hyperbolic topology and the metric topology coincide on X if and only if the Lawson topology and the product topology coincide on BX
Computation on metric spaces via domain theory
The purpose of this paper is to survey recent approaches to realizing (or embedding) a Polish space as the set of maximal points of a continuous domain. Such realizations provide a convenient framework in which to model certain computational algorithms on the space and a useful alternate approach via the probabilistic power domain to measure theory and integraion on the space. © 1998 Elsevier Science B.V
06341 Abstracts Collection -- Computational Structures for Modelling Space, Time and Causality
From 20.08.06 to 25.08.06, the Dagstuhl Seminar 06341 ``Computational Structures for Modelling Space, Time and Causality\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Stringy Instability of Topologically Non-Trivial Ads Black Holes and of desitter S-Brane Spacetimes
Seiberg and Witten have discussed a specifically "stringy" kind of
instability which arises in connection with "large" branes in asymptotically
AdS spacetimes. It is easy to see that this instability actually arises in most
five-dimensional asymptotically AdS black hole string spacetimes with
non-trivial horizon topologies. We point out that this is a more serious
problem than it may at first seem, for it cannot be resolved even by taking
into account the effect of the branes on the geometry of spacetime. [It is
ultimately due to the {\em topology} of spacetime, not its geometry.] Next,
assuming the validity of some kind of dS/CFT correspondence, we argue that
asymptotically deSitter versions of the Hull-Strominger-Gutperle S-brane
spacetimes are also unstable in this "topological" sense, at least in the case
where the R-symmetries are preserved. We conjecture that this is due to the
unrestrained creation of "late" branes, the spacelike analogue of large branes,
at very late cosmological times.Comment: References added, NPB versio
- …