Order Topology

A topology defined on a totally ordered set X whose open sets are all the finite intersections of subsets of the form {x in X|x>a} or {x in X|x<a}, where a in X.

The order topology of the real line is the Euclidean topology. The order topology of N is the discrete topology, since for all n in N,

 {n}={x in N|x>n-1} intersection {x in N|x<n+1}

is an open set.

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Order Topology." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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