"pointless topology" meaning in English

{
  "forms": [
    {
      "form": "pointless topologies",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-",
        "2": "+"
      },
      "expansion": "pointless topology (usually uncountable, plural pointless 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": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "coordinate_terms": [
        {
          "word": "point-set topology"
        }
      ],
      "examples": [
        {
          "ref": "1995, Francis Buekenhout, editor, Handbook of Incidence Geometry: Buildings and Foundations, North-Holland: Elsevier, page 1018",
          "text": "The works of Ehresmann [1957/58], Benabou [1957/58], Papert and Papert [1957/58] give rise to pointless topology, i.e. an abstract treatment of a class of lattices (the frames) extending the class whose members are the lattices of open sets of the topological spaces.",
          "type": "quotation"
        },
        {
          "text": "1997, Stephen C. Hirtle, Andrew U. Frank (editors), Spatial Information Theory A Theoretical Basis for GIS: International Conference COSIT '97, Proceedings, Springer, LNCS 1329, page 170,\nPointless topology is more general than point-set topology in that there are complete Heyting algebras which do not come from the open set lattices of topological spaces."
        },
        {
          "text": "2001, Peter Johnstone, Elements of the History of Locale Theory, C.E. Aull, R. Lowen (editors), Handbook of the History of General Topology, Volume 3, Kluwer Academic, page 841,\nBanaschewski was to become one of the most prolific authors on pointless topology, and in particular on its constructive and choice-free aspects, in the next three decades."
        }
      ],
      "glosses": [
        "An approach to topology that avoids mentioning points."
      ],
      "id": "en-pointless_topology-en-noun-b3aTb6IL",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "topology",
          "topology"
        ],
        [
          "point",
          "point"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An approach to topology that avoids mentioning points."
      ],
      "synonyms": [
        {
          "sense": "approach to topology",
          "word": "locale theory"
        },
        {
          "sense": "approach to topology",
          "word": "pointfree topology"
        }
      ],
      "tags": [
        "uncountable",
        "usually"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "pointless topology"
      ]
    }
  ],
  "word": "pointless topology"
}

{
  "coordinate_terms": [
    {
      "word": "point-set topology"
    }
  ],
  "forms": [
    {
      "form": "pointless topologies",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-",
        "2": "+"
      },
      "expansion": "pointless topology (usually uncountable, plural pointless topologies)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "1995, Francis Buekenhout, editor, Handbook of Incidence Geometry: Buildings and Foundations, North-Holland: Elsevier, page 1018",
          "text": "The works of Ehresmann [1957/58], Benabou [1957/58], Papert and Papert [1957/58] give rise to pointless topology, i.e. an abstract treatment of a class of lattices (the frames) extending the class whose members are the lattices of open sets of the topological spaces.",
          "type": "quotation"
        },
        {
          "text": "1997, Stephen C. Hirtle, Andrew U. Frank (editors), Spatial Information Theory A Theoretical Basis for GIS: International Conference COSIT '97, Proceedings, Springer, LNCS 1329, page 170,\nPointless topology is more general than point-set topology in that there are complete Heyting algebras which do not come from the open set lattices of topological spaces."
        },
        {
          "text": "2001, Peter Johnstone, Elements of the History of Locale Theory, C.E. Aull, R. Lowen (editors), Handbook of the History of General Topology, Volume 3, Kluwer Academic, page 841,\nBanaschewski was to become one of the most prolific authors on pointless topology, and in particular on its constructive and choice-free aspects, in the next three decades."
        }
      ],
      "glosses": [
        "An approach to topology that avoids mentioning points."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "topology",
          "topology"
        ],
        [
          "point",
          "point"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An approach to topology that avoids mentioning points."
      ],
      "tags": [
        "uncountable",
        "usually"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "pointless topology"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "approach to topology",
      "word": "locale theory"
    },
    {
      "sense": "approach to topology",
      "word": "pointfree topology"
    }
  ],
  "word": "pointless topology"
}