An Upper Power Domain Construction in Terms of Strongly Compact Sets

@inproceedings{Heckmann1991AnUP,
  title={An Upper Power Domain Construction in Terms of Strongly Compact Sets},
  author={Reinhold Heckmann},
  booktitle={Mathematical Foundations of Programming Semantics},
  year={1991}
}
  • Reinhold Heckmann
  • Published in
    Mathematical Foundations of…
    25 March 1991
  • Mathematics
A novel upper power domain construction is defined by means of strongly compact sets. Its power domains contain less elements than the classical ones in terms of compact sets, but still admit all necessary operations, i.e. they contain less junk. The notion of strong compactness allows a proof of stronger properties than compactness would, e.g. an intrinsic universal property of the upper power construction, and its commutation with the lower construction. 

Stable Power Domains

On the commutativity of the powerspace constructions

It is shown that the upper and lower powerspaces commute on all quasi-Polish spaces, and more generally that this commutativity is equivalent to the topological property of consonance.

Power structures of directed spaces

Powerdomains in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages. In this paper, we extend the notion of powerdomain to the

Observable modules and power domain constructions

An R-module M is observable ii all its elements can be distinguished by observing them by means of linear morphisms from M to R. We show that free observable R-modules can be explicitly described as

On Scott power spaces

In this paper, we mainly discuss some basic properties of Scott power spaces. For a T 0 space X , let K ( X ) be the poset of all nonempty compact saturated subsets of X endowed with the Smyth order.

On Some Topological Properties of Dcpo Models of $$T_1$$ Topological Spaces

. We prove that a T 1 space X is a Rudin space if and only if its Xi-Zhao model D ( X ) is a Rudin space and that a T 1 space is weak sober if and only if it has a weak sober dcpo model. It is also
...

References

SHOWING 1-10 OF 13 REFERENCES

Power Domain Constructions

Cartesian closed categories of domains

2.3 The two maximal cartesian closed categories of algebraic directed-complete partial orders with a least 1 3.3 The four maximal cartesian closed categories of algebraic directed-1.4 An algebraic

A Powerdomain Construction

  • G. Plotkin
  • Computer Science, Mathematics
    SIAM J. Comput.
  • 1976
A powerdomain construction is developed, which is analogous to the powerset construction and also fits in with the usual sum, product and exponentiation constructions on domains, and a restricted class of algebraic inductive partial orders is found which is closed under this construction.

Power Domains and Predicate Transformers: A Topological View

The specific tasks are to provide a more adequate framework for power-domain constructions; and to show that the connection between (Dijkstra's) weakest preconditions and the Smyth powerdomain, established by Plotkin for the case of flat domains, actually holds in full generality.

A Compendium of Continuous Lattices

O. A Primer of Complete Lattices.- 1. Generalities and notation.- 2. Complete lattices.- 3. Galois connections.- 4. Meet-continuous lattices.- I. Lattice Theory of Continuous Lattices.- 1. The

Full Abstraction for a Simple Parallel Programming Language

A denotational semantics for a simple language with parallelism was given, treating parallelism in terms of non-deterministic mergeing of uninterruptible actions, and expected identities such as the associativity and commutativity of the parallel combinator were true in this semantics.

Power Domains

  • M. Smyth
  • Mathematics
    J. Comput. Syst. Sci.
  • 1978