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Can I read Some results on Hahn–Banach-type theorems for continuous D-cones on EtoBox?
Some results on Hahn–Banach-type theorems for continuous D-cones by Regina Tix is a Computer Science article available to read on EtoBox.
What is Some results on Hahn–Banach-type theorems for continuous D-cones about?
Like the extended non-negative reals R+ equipped with the Scott topology, there are other real topological cones such that the specialisation order yields a directed complete partially ordered set (dcpo). We will call them d-cones. Further examples are the extended probabilistic powerdomain, the set of all lower semicontinuous functions f : X → R+ for any topological space X and arbitrary products of given d-cones. The dual cone C \* for a given d-cone C consists of all linear continuous functions : C → R+. With respect to the pointwise order, addition and scalar multiplication the dual cone becomes also a d-cone. We are interested in obtaining results with our concept of d-cones that are comparable to Hahn-Banach-type theorems in functional analysis. Indeed, we can prove an Extension Theorem and a Separation Theorem for the continuous d-cones. In particular, the second implies that the elements of the dual cone C \* separate the points of C. As a consequence of the Extension Theorem, we obtain a Sum Theorem for continuous d-cones. We will give some su cient conditions when the previous examples of d-cones are continuous and have an additive way-below relation.
Who reads Some results on Hahn–Banach-type theorems for continuous D-cones?
It is typically read by researchers, students, and practitioners in Computer Science.
- Author
- Regina Tix
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0304-3975)
- Published
- 2001
- Language
- EN
- Field
- Computer Science (Physical Sciences)