What's the English terminology for a "section" set?

Asked May 19 '19 at 20:32

Active May 19 '19 at 21:56

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I'm translating the terminology from my native language into English. The closest placeholder I have to the word is a "section" set, but I couldn't find anything like that online.

We say that $A \subseteq \mathbb{Q}$ is a section if it does not contain a maximal member, and that every $a \in A$ and every $q\in \mathbb{Q}$ allow for:

$x \leq a \Rightarrow x \in A$

edited May 19 '19 at 21:56

Asaf Karagila

393,674

asked May 19 '19 at 20:32

daedsidog

Downward closed possibly? – bsbb4 May 19 '19 at 20:38
4

If additionally $A\ne\emptyset$ and $A\ne\Bbb Q$, this looks like a Dedekind cut. – Hagen von Eitzen May 19 '19 at 20:42
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@HagenvonEitzen Yes, that's it. The definition fits. Also think the definition may be flawed, as $x$ should be replaced with $q$. – daedsidog May 19 '19 at 20:43
Section is also used in English. – Matt Samuel May 19 '19 at 20:49

What's the English terminology for a "section" set?

0 Answers0