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Order Relation

  • Definition: A relation C on a set A is called an order relation (or a simple order, or a linear order) if it has the following properties: 1) (Comparability) For every x and y in A for which x does not equal y, either xCy or yCx. 2) (Nonreflexivity) For no x in A does the relation xCx hold. 3) (Transitivity) If xCy and yCz, then xCz.

    Source: Topology (second edition) by James R. Munkres

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