2,761 research outputs found
Topology in Computer Science: Constructivity; Asymmetry and Partiality; Digitization (Dagstuhl Seminar 00231)
No full text
What do partial metrics represent?
No full textPartial metrics were introduced in 1992
as a metric to allow the distance of a point from
itself to be non zero. This notion of self distance, designed to extend
metrical concepts to Scott topologies as used
in computing, has little intuition for the mainstream Hausdorff topologist.
The talk will show that a partial metric over a set can be represented by a metric over that set with a so-called 'base point'.
Thus we establish that a partial metric is essentially a structure combining both a metric space and a skewed view of that space from the base point. From this we can deduce what it is that partial metrics are really all about
The topology of partial metric spaces
No full textThe T0 world of Scott's topological models used in the denotational semantics of programming languages may at first sight appear to have nothing whatever in common with the Hausdorff world of metric space theory. Can this be true though when the notion of "distance" is so important in the application of inductive proof theory to recursive definitions? This paper shows that existing work on the application of quasi metrics to denotational semantics can be taken much further than just describing Scott topologies. Using our "partial metric" we introduce a new approach by constructing each semantic domain as an Alexandrov topology "sandwiched" between two metric topologies. To be presented at the Eighth Summer Conference on General Topology and Applications, June 18-20 1992, Queens College, New York City
06341 Abstracts Collection – Computational Structures for Modelling Space, Time and Causality
No full textFrom 20.08.06 to 25.08.06, the Dagstuhl Seminar 06341 ``Computational Structures for Modelling Space, Time and Causality'' 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
Auxiliary relations and sandwich theorems
No full textA well-known topological theorem due to Kat\v etov states:
Suppose is a normal topological space, and let be upper semicontinuous, be lower semicontinuous, and . Then there is a continuous such that .
We show a version of this theorem for many posets with auxiliary relations. In particular, if is a Scott domain and are such that , and is lower continuous and Scott continuous, then for some , and is both Scott and lower continuous.
As a result, each Scott continuous function from to , is the sup of the functions below it which are both Scott and lower continuous
04351 Summary – Spatial Representation: Discrete vs. Continuous Computational Models
No full textTopological notions and methods are used in various areas of the physical sciences and engineering, and therefore computer processing of topological data is important. Separate from this, but closely related, are computer science uses of topology: applications to programming language semantics and computing with exact real numbers are important examples. The seminar concentrated on an important approach, which is basic to all these applications, i.e. spatial representation
Letter from Ralph H. Cameron to Carl Hayden
No full textLetter from Ralph H. Cameron asking to speak to Carl Hayden concerning a matter relevant to the bill granting National Park status to the Grand Canyon
04351 Abstracts Collection – Spatial Representation: Discrete vs. Continuous Computational Models
No full textFrom 22.08.04 to 27.08.04, the Dagstuhl Seminar 04351
``Spatial Representation: Discrete vs. Continuous Computational Models''
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
Letter from Carl Hayden to Ralph H. Cameron
No full textLetter from Carl Hayden to Ralph H. Cameron responding favorably to a request to meet in regards to the bill granting National Park status to the Grand Canyon
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