Timeline for scott continuity, sub additivity
Current License: CC BY-SA 3.0
3 events
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| Oct 16, 2014 at 12:43 | comment | added | Dominic van der Zypen | Right, thanks for your remark -- and it is important to replace "monotone" by "the supremum of $f(D)$ exists" (just as you did). But I agree that your version is more economical | |
| Oct 16, 2014 at 12:40 | comment | added | polmath | dominiczypen: just a kind remark, you don't need to assume that $f$ is monotone in your definition of a Scott-continuous map, if one rephrases a bit the definition as follows: $f$ is Scott-continuous if for every non-empty directed subset $D$, the supremum of $f(D)$ exists and equals $f(\bigvee D)$. (Then $f$ is necessarily monotone.) | |
| Oct 16, 2014 at 7:25 | history | answered | Dominic van der Zypen | CC BY-SA 3.0 |