Order topology (functional analysis)
= Order topology (functional analysis)
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In functional analysis and general topology, the **order topology** is a way to define a topology on a set that is equipped with a total order. This topology is constructed from the order properties of the set, allowing us to study the convergence and continuity of functions in that ordered set. \#\#\# Definition: Let \\( X \\) be a set equipped with a total order \\( \\leq \\).