Definition:Continuous Total Preordering
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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 $\left\langle{a^k}\right\rangle_k$ and $\left\langle{b^k}\right\rangle_k$ 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): $1.7$: Terminology and Notation