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Non-Hausdorff Topology and Domain Theory by Jean Goubault-Larrecq

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5

Approximation and function spaces

In Section 4.2.2, we discussed how computer programs could be thought of as computing values x obtained as supnϵimage xn, where xn are values in a given dcpo, e.g., the dcpo of sets of formulae in the example of the automated theoremproving computer. A distinguishing feature of the approximants xn to x is that they are finite, and this particular relation between xn and x can be described in arbitrary posets by saying that xn is way-below x. The way-below relation image is a fundamental notion, leading to so-called continuous ...

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