Ordinal optimization: Difference between revisions

Revision as of 15:08, 27 May 2021

Revision as of 08:26, 27 October 2021

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* The set of [[subset]]s of a given set (its [[power set]]) ordered by [[subset|inclusion]]

* The set of subspaces of a [[vector space]] ordered by inclusion.

* For a partially ordered set ''P'', the [[sequence space]] containing all [[sequence]]s of elements from ''P'', where sequence ''a'' precedes sequence ''b'' if every item in ''a'' precedes the corresponding item in ''b''. Formally, {{math|(''a''_''n'')_{''n''∈ℕ∈<math>\mathbb{N}</math>}&nbsp;≤&nbsp;(''b''_''n'')_{''n''∈ℕ∈<math>\mathbb{N}</math>}}} if and only if {{math|''a''_''n''&nbsp;≤&nbsp;''b''_''n''}} for all ''n'' in ℕ<math>\mathbb{N}</math>.

* For a set ''X'' and a partially ordered set ''P'', the [[function space]] containing all functions from ''X'' to ''P'', where ''f'' ≤ ''g'' if and only if ''f''(''x'') ≤ ''g''(''x'') for all ''x'' in ''X''.

* The vertex set of a [[directed acyclic graph]] ordered by [[reachability]].