"Alexandrov topology" meaning in All languages combined

{
  "etymology_text": "Along with the closely related concept of Alexandrov-discrete space, after Russian mathematician Pavel Sergeyevich Alexandrov.",
  "forms": [
    {
      "form": "Alexandrov topologies",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Alexandrov topology (plural Alexandrov topologies)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
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          "source": "w"
        },
        {
          "kind": "other",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1972, Roger Penrose, Techniques of Differential Topology in Relativity, SIAM, page 34:",
          "text": "4.24. THEOREM. The following three restrictions on a space-time M are equivalent:\n(a) M is strongly causal;\n(b) the Alexandrov topology agrees with the manifold topology;\n(c) the Alexandrov topology is Hausdorff.",
          "type": "quote"
        },
        {
          "ref": "1990, Palle Yourgrau, Demonstratives, Oxford University Press, page 252:",
          "text": "In Minkowski space-time there is, indeed, a topology definable solely in terms of the causal connectivity among events, the Alexandrov topology, which is provably equivalent to the ordinary manifold topology.",
          "type": "quote"
        },
        {
          "text": "2016, Piero Pagliani, Covering Rough Sets and Formal Topology — A Uniform Approach Through Intensional and Extensional Operators, James F. Peters, Andrzej Skowron (editors), Transactions on Rough Sets XX, Springer, LNCS 10020, page 134,\n(6) S_0,2(P(R_C)) is the family of open sets of the Alexandrov topology induced by R_C and S(P(R_C)) is the family of closed sets of the Alexandrov topology induced by R^⌣_C;"
        }
      ],
      "glosses": [
        "A topology in which the intersection of any family of open sets is an open set."
      ],
      "id": "en-Alexandrov_topology-en-noun-UaefE7-Z",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "intersection",
          "intersection"
        ],
        [
          "open set",
          "open set"
        ]
      ],
      "raw_glosses": [
        "(topology) A topology in which the intersection of any family of open sets is an open set."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ],
      "wikipedia": [
        "Alexandrov topology",
        "Pavel Sergeyevich Alexandrov"
      ]
    }
  ],
  "word": "Alexandrov topology"
}

{
  "etymology_text": "Along with the closely related concept of Alexandrov-discrete space, after Russian mathematician Pavel Sergeyevich Alexandrov.",
  "forms": [
    {
      "form": "Alexandrov topologies",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Alexandrov topology (plural Alexandrov topologies)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English countable nouns",
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        "English multiword terms",
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        "Pages with 1 entry",
        "Pages with entries",
        "en:Topology"
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      "examples": [
        {
          "ref": "1972, Roger Penrose, Techniques of Differential Topology in Relativity, SIAM, page 34:",
          "text": "4.24. THEOREM. The following three restrictions on a space-time M are equivalent:\n(a) M is strongly causal;\n(b) the Alexandrov topology agrees with the manifold topology;\n(c) the Alexandrov topology is Hausdorff.",
          "type": "quote"
        },
        {
          "ref": "1990, Palle Yourgrau, Demonstratives, Oxford University Press, page 252:",
          "text": "In Minkowski space-time there is, indeed, a topology definable solely in terms of the causal connectivity among events, the Alexandrov topology, which is provably equivalent to the ordinary manifold topology.",
          "type": "quote"
        },
        {
          "text": "2016, Piero Pagliani, Covering Rough Sets and Formal Topology — A Uniform Approach Through Intensional and Extensional Operators, James F. Peters, Andrzej Skowron (editors), Transactions on Rough Sets XX, Springer, LNCS 10020, page 134,\n(6) S_0,2(P(R_C)) is the family of open sets of the Alexandrov topology induced by R_C and S(P(R_C)) is the family of closed sets of the Alexandrov topology induced by R^⌣_C;"
        }
      ],
      "glosses": [
        "A topology in which the intersection of any family of open sets is an open set."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "intersection",
          "intersection"
        ],
        [
          "open set",
          "open set"
        ]
      ],
      "raw_glosses": [
        "(topology) A topology in which the intersection of any family of open sets is an open set."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ],
      "wikipedia": [
        "Alexandrov topology",
        "Pavel Sergeyevich Alexandrov"
      ]
    }
  ],
  "word": "Alexandrov topology"
}