Two Counterexamples Concerning the Scott Topology on a Partial Order
نویسنده
چکیده
We construct a complete lattice Z such that the binary supremum function sup : Z × Z → Z is discontinuous with respect to the product topology on Z × Z of the Scott topologies on each copy of Z. In addition, we show that bounded completeness of a complete lattice Z is in general not inherited by the dcpo C(X,Z) of continuous functions from X to Z where X may be any topological space and where on Z the Scott topology is considered.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1607.04128 شماره
صفحات -
تاریخ انتشار 2016