Triple

T5425860
Position Surface form Disambiguated ID Type / Status
Subject Ernst Lindelöf E121359 entity
Predicate hasConceptNamedAfter P3325 FINISHED
Object Lindelöf space
A Lindelöf space is a topological space in which every open cover has a countable subcover, generalizing a key compactness property.
E518483 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Lindelöf space | Statement: [Ernst Lindelöf, hasConceptNamedAfter, Lindelöf space]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lindelöf space
Context triple: [Ernst Lindelöf, hasConceptNamedAfter, Lindelöf space]
  • A. Alexandrov–Hausdorff theorem
    The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
  • B. Hausdorff
    Hausdorff is a topological separation property requiring that any two distinct points in a space can be enclosed in disjoint open sets.
  • C. Noetherian space
    A Noetherian space is a topological space in which every descending chain of closed subsets stabilizes, mirroring the finiteness conditions of Noetherian rings in algebra.
  • D. Tychonoff theorem for products of compact spaces
    The Tychonoff theorem for products of compact spaces is a fundamental result in topology stating that any product of compact topological spaces is compact, a statement that is equivalent in strength to the axiom of choice.
  • E. Alexandrov compactification
    The Alexandrov compactification is a topological construction that adds a single “point at infinity” to a non-compact space to make it compact.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Lindelöf space
Triple: [Ernst Lindelöf, hasConceptNamedAfter, Lindelöf space]
Generated description
A Lindelöf space is a topological space in which every open cover has a countable subcover, generalizing a key compactness property.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lindelöf space
Target entity description: A Lindelöf space is a topological space in which every open cover has a countable subcover, generalizing a key compactness property.
  • A. Alexandrov–Hausdorff theorem
    The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
  • B. Hausdorff
    Hausdorff is a topological separation property requiring that any two distinct points in a space can be enclosed in disjoint open sets.
  • C. Noetherian space
    A Noetherian space is a topological space in which every descending chain of closed subsets stabilizes, mirroring the finiteness conditions of Noetherian rings in algebra.
  • D. Tychonoff theorem for products of compact spaces
    The Tychonoff theorem for products of compact spaces is a fundamental result in topology stating that any product of compact topological spaces is compact, a statement that is equivalent in strength to the axiom of choice.
  • E. Alexandrov compactification
    The Alexandrov compactification is a topological construction that adds a single “point at infinity” to a non-compact space to make it compact.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69bd463b58d88190b258261573de9e91 completed March 20, 2026, 1:06 p.m.
NER Named-entity recognition batch_69bd881598448190a9bb456dee36004b completed March 20, 2026, 5:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69bf3abfc7e88190b8f0a31b61c33973 completed March 22, 2026, 12:41 a.m.
NEDg Description generation batch_69bf3b592a08819090e2873bcf4e797f completed March 22, 2026, 12:44 a.m.
NED2 Entity disambiguation (via description) batch_69bf3c0b9e5481909101eccbd55f24b2 completed March 22, 2026, 12:47 a.m.
Created at: March 20, 2026, 2:06 p.m.