NoteA note on “Posets having continuous interval”
Section snippets
Counterexample
For all the basic concepts and notations of this note the main reference is [1].
The result for which we will present a counterexample is: Proposition 1.1 Let P be a continuous poset such that (i) Each interval of P is a sup-semilattice and (ii) Each principal ideal has a (necessarily unique) smallest element. For a core compact space X, each principal ideal of is a continuous poset and a sup-semilattice with smallest element. If additionally P is a dcpo, then is a continuous dcpo.[2]
In [2], this
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was partially financed by funding agency CAPES Brazil - Finance Code 001. (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior).
References (2)
- et al.
Posets having continuous intervals
Theor. Comp. Sci.
(2004) - et al.
Continuous Lattices and Domains
(2003)