"rel" meaning in English

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      "expansion": "rel",
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      "args": {},
      "expansion": "rel",
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  "lang": "English",
  "lang_code": "en",
  "pos": "prep",
  "senses": [
    {
      "alt_of": [
        {
          "word": "relative to"
        }
      ],
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          "source": "w"
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          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
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      "examples": [
        {
          "ref": "1994, N[ikita] Netsvetaev, “Diffeomorphism Criteria for Simply Connected Even-Dimensional Manifolds”, in Oleg Viro, editor, Topology of Manifolds and Varieties (Advances in Soviet Mathematics [series] 18), American Mathematical Society, →ISBN, page 237:",
          "text": "Since M#x5F;0 and M#x5F;1 are cobordant rel boundary and f#x5F;0,f#x5F;1 are n-connected, the number #x5C;delta#x3A;#x3D;#x5C;frac12(#x5C;mathrm#x7B;rk#x7D;H#x5F;nM#x5F;0-#x5C;mathrm#x7B;rk#x7D;H#x5F;nM#x5F;1) is a nonnnegative integer.",
          "type": "quote"
        },
        {
          "ref": "1997, Paul Selick, Introduction to Homotopy Theory (Fields Institute Monographs), American Mathematical Society, →ISBN, page 15:",
          "text": "The following notations are in common use: H#x3A;f#x5C;simeqg (rel A) means that H is a homotopy rel A from f to g....",
          "type": "quote"
        },
        {
          "ref": "2002, Allen Hatcher, Algebraic Topology, Cambridge, →ISBN, page 355:",
          "text": "Then in n#x5C;gen', there is a map h#x3A;Z#x5C;toZ' such that h#x7C;A#x3D;g and gf#x5C;simeqf'h rel A, so the diagram above is commutative up to homotopy rel A.",
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        "Abbreviation of relative to."
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          "relative",
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        "(mathematics) Abbreviation of relative to."
      ],
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      "topics": [
        "mathematics",
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  "word": "rel"
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          "word": "relative to"
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          "ref": "1994, N[ikita] Netsvetaev, “Diffeomorphism Criteria for Simply Connected Even-Dimensional Manifolds”, in Oleg Viro, editor, Topology of Manifolds and Varieties (Advances in Soviet Mathematics [series] 18), American Mathematical Society, →ISBN, page 237:",
          "text": "Since M#x5F;0 and M#x5F;1 are cobordant rel boundary and f#x5F;0,f#x5F;1 are n-connected, the number #x5C;delta#x3A;#x3D;#x5C;frac12(#x5C;mathrm#x7B;rk#x7D;H#x5F;nM#x5F;0-#x5C;mathrm#x7B;rk#x7D;H#x5F;nM#x5F;1) is a nonnnegative integer.",
          "type": "quote"
        },
        {
          "ref": "1997, Paul Selick, Introduction to Homotopy Theory (Fields Institute Monographs), American Mathematical Society, →ISBN, page 15:",
          "text": "The following notations are in common use: H#x3A;f#x5C;simeqg (rel A) means that H is a homotopy rel A from f to g....",
          "type": "quote"
        },
        {
          "ref": "2002, Allen Hatcher, Algebraic Topology, Cambridge, →ISBN, page 355:",
          "text": "Then in n#x5C;gen', there is a map h#x3A;Z#x5C;toZ' such that h#x7C;A#x3D;g and gf#x5C;simeqf'h rel A, so the diagram above is commutative up to homotopy rel A.",
          "type": "quote"
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      "glosses": [
        "Abbreviation of relative to."
      ],
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          "relative",
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        "(mathematics) Abbreviation of relative to."
      ],
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