Total order
noun ·Rare ·Advanced level
Definitions
- 1 A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x).
"[…]we conclude §2.1 by showing how, given a triangulation #92;Delta (i.e., simplicial decomposition) of a closed oriented 3-manifilld M, and a total order '#92;le' on the set of vertices of #92;Delta, as well as a choice of a system #92;mathcal#123;B#125; of orthonormal bases for various Hilbert spaces that get specified in the process, we may obtain a complex number #92;langle(M,#92;Delta,#92;le,#92;mathcal#123;B#125;)#92;rangle."
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More examples"[…]we conclude §2.1 by showing how, given a triangulation #92;Delta (i.e., simplicial decomposition) of a closed oriented 3-manifilld M, and a total order '#92;le' on the set of vertices of #92;Delta, as well as a choice of a system #92;mathcal#123;B#125; of orthonormal bases for various Hilbert spaces that get specified in the process, we may obtain a complex number #92;langle(M,#92;Delta,#92;le,#92;mathcal#123;B#125;)#92;rangle."