EDB — 2FJ

Direct and filtering order[2FJ]

The sets \(ℝ,ℕ,ℚ,ℤ\) endowed with their usual order relations, are filtering.

Obviously a filtering order is direct.

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[06Q]↺↻

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[06S]↺↻

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[06V]↺↻

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[06X]↺↻

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[232]↺↻

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[234]↺↻

A directed ordered set \((X,≤)\) is a framework in which we can generalize the notion seen in [018]↺↻.

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[070]↺↻

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[233]↺↻

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[06Z]↺↻

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[2B2]↺↻

Further exercises on the subject are [29J]↺↻,[0GQ]↺↻, and in Section [29X]↺↻.