"Alexandrov topology" meaning in English

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "Alexandrov-discrete space"
      },
      "expansion": "Alexandrov-discrete space",
      "name": "m"
    }
  ],
  "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"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "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": "quotation"
        },
        {
          "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": "quotation"
        },
        {
          "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_templates": [
    {
      "args": {
        "1": "en",
        "2": "Alexandrov-discrete space"
      },
      "expansion": "Alexandrov-discrete space",
      "name": "m"
    }
  ],
  "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": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English terms with quotations",
        "en:Topology"
      ],
      "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": "quotation"
        },
        {
          "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": "quotation"
        },
        {
          "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"
}