In mathematics, the upper topology on a partially ordered set X is the coarsest topology in which the closure of a singleton { a } {\displaystyle \{a\}} is the order section a ] = { x ≤ a } {\displaystyle a]=\{x\leq a\}} for each a ∈ X . {\displaystyle a\in X.} If ≤ {\displaystyle \leq } is a partial order, the upper topology is the least order consistent topology in which all open sets are up-sets.
In mathematics, the upper topology on a partially ordered set X is the coarsest topology in which the closure of a singleton { a } {\displaystyle \{a\}} is the order section a ] = { x ≤ a } {\displaystyle a]=\{x\leq a\}} for each a ∈ X . {\displaystyle a\in X.} If ≤ {\displaystyle \leq } is a partial order, the upper topology is the least order consistent topology in which all open sets are up-sets.
Source: Wikipedia "Upper topology" · CC BY-SA 4.0
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