Monotone Net
# Definition 1
Let $X$ be a Partial Ordering and $I$ a Nonempty Directed Partial Ordering Index Set. We call a Net $(x_{\alpha}){\alpha \in I} \subset X$ a Monotone Net if $x{\bullet}: I \to X$ is a Monotone Function.
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Let $X$ be a Partial Ordering and $I$ a Nonempty Directed Partial Ordering Index Set. We call a Net $(x_{\alpha}){\alpha \in I} \subset X$ a Monotone Net if $x{\bullet}: I \to X$ is a Monotone Function.