Definition:Continuous Total Preordering

Definition

Let $S$ be a set.

Let $\precsim$ be a total preordering on $S$.

Let $\precsim$ be such that:

$a \precsim b$ whenever there exist sequences $\sequence {a^k}_k$ and $\sequence {b^k}_k$ that converge to $a$ and $b$ respectively for which $a^k \precsim b^k$ for all $k$.

Then $\precsim$ is continuous.

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Sources

• 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): Chapter $1$ Introduction: $1.7$: Terminology and Notation