"bilattice" meaning in English

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  "etymology_text": "bi- + lattice",
  "forms": [
    {
      "form": "bilattices",
      "tags": [
        "plural"
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      "expansion": "bilattice (plural bilattices)",
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  "lang_code": "en",
  "pos": "noun",
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      "examples": [
        {
          "ref": "2015, Janko Bračič, Lina Oliveira, “A characterization of reflexive spaces of operators”, in arXiv",
          "text": "We show that for a linear space of operators #x7B;#x5C;mathcalM#x7D;#x5C;subseteq#x7B;#x5C;mathcalB#x7D;(H#x5F;1,H#x5F;2) the following assertions are equivalent. (i) #x7B;#x5C;mathcalM#x7D; is reflexive in the sense of Loginov--Shulman. (ii) There exists an order-preserving map 1 on a bilattice Bil(#x7B;#x5C;mathcalM#x7D;) of subspaces determined by #x7B;#x5C;mathcalM#x7D;, with P#x5C;leq#x5C;psi#x5F;1(P,Q) and Q#x5C;leq#x5C;psi#x5F;2(P,Q), for any pair (P,Q)#x5C;inBil(#x7B;#x5C;mathcalM#x7D;), and such that an operator T#x5C;in#x7B;#x5C;mathcalB#x7D;(H#x5F;1,H#x5F;2) lies in #x7B;#x5C;mathcalM#x7D; if and only if #x5C;psi#x5F;2(P,Q)T#x5C;psi#x5F;1(P,Q)#x3D;0 for all (P,Q)#x5C;inBil(#x7B;#x5C;mathcalM#x7D;).",
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      "glosses": [
        "A structure B = (S,⊑₁ ,⊑₂) in which S is a non-empty set, and ⊑₁ and ⊑₂ are partial orderings each giving S the structure of a lattice, determining thus for each of the two lattices the corresponding operations of meet and join."
      ],
      "id": "en-bilattice-en-noun-gBiXkDfm",
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          "mathematics",
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          "computing#Noun"
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      "raw_glosses": [
        "(mathematics, computing) A structure B = (S,⊑₁ ,⊑₂) in which S is a non-empty set, and ⊑₁ and ⊑₂ are partial orderings each giving S the structure of a lattice, determining thus for each of the two lattices the corresponding operations of meet and join."
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  "word": "bilattice"
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  "etymology_text": "bi- + lattice",
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    {
      "form": "bilattices",
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  "lang_code": "en",
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          "ref": "2015, Janko Bračič, Lina Oliveira, “A characterization of reflexive spaces of operators”, in arXiv",
          "text": "We show that for a linear space of operators #x7B;#x5C;mathcalM#x7D;#x5C;subseteq#x7B;#x5C;mathcalB#x7D;(H#x5F;1,H#x5F;2) the following assertions are equivalent. (i) #x7B;#x5C;mathcalM#x7D; is reflexive in the sense of Loginov--Shulman. (ii) There exists an order-preserving map 1 on a bilattice Bil(#x7B;#x5C;mathcalM#x7D;) of subspaces determined by #x7B;#x5C;mathcalM#x7D;, with P#x5C;leq#x5C;psi#x5F;1(P,Q) and Q#x5C;leq#x5C;psi#x5F;2(P,Q), for any pair (P,Q)#x5C;inBil(#x7B;#x5C;mathcalM#x7D;), and such that an operator T#x5C;in#x7B;#x5C;mathcalB#x7D;(H#x5F;1,H#x5F;2) lies in #x7B;#x5C;mathcalM#x7D; if and only if #x5C;psi#x5F;2(P,Q)T#x5C;psi#x5F;1(P,Q)#x3D;0 for all (P,Q)#x5C;inBil(#x7B;#x5C;mathcalM#x7D;).",
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      "glosses": [
        "A structure B = (S,⊑₁ ,⊑₂) in which S is a non-empty set, and ⊑₁ and ⊑₂ are partial orderings each giving S the structure of a lattice, determining thus for each of the two lattices the corresponding operations of meet and join."
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        "(mathematics, computing) A structure B = (S,⊑₁ ,⊑₂) in which S is a non-empty set, and ⊑₁ and ⊑₂ are partial orderings each giving S the structure of a lattice, determining thus for each of the two lattices the corresponding operations of meet and join."
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  "word": "bilattice"
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