"Topologie" (with W. Hurewicz)
E679327
"Topologie" (with W. Hurewicz) is a foundational textbook in topology co-authored by Heinz Hopf and Witold Hurewicz that helped shape the modern development and teaching of the subject.
All labels observed (1)
| Label | Occurrences |
|---|---|
| "Topologie" (with W. Hurewicz) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7648338 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: "Topologie" (with W. Hurewicz) Context triple: [Heinz Hopf, notablePublication, "Topologie" (with W. Hurewicz)]
-
A.
Topologie (with Heinz Hopf)
"Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
-
B.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
C.
Moscow school of topology
The Moscow school of topology was a prominent mathematical tradition centered in Moscow that made foundational contributions to general and algebraic topology in the 20th century.
-
D.
"Algebraic Topology"
"Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
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E.
L’Analysis Situs et la Géométrie Algébrique
L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: "Topologie" (with W. Hurewicz) Target entity description: "Topologie" (with W. Hurewicz) is a foundational textbook in topology co-authored by Heinz Hopf and Witold Hurewicz that helped shape the modern development and teaching of the subject.
-
A.
Topologie (with Heinz Hopf)
"Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
-
B.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
C.
Moscow school of topology
The Moscow school of topology was a prominent mathematical tradition centered in Moscow that made foundational contributions to general and algebraic topology in the 20th century.
-
D.
"Algebraic Topology"
"Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
-
E.
L’Analysis Situs et la Géométrie Algébrique
L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
- F. None of above. chosen
Statements (24)
| Predicate | Object |
|---|---|
| instanceOf |
academic book
ⓘ
reference work ⓘ topology textbook ⓘ |
| audience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ |
| author |
Heinz Hopf
ⓘ
Witold Hurewicz ⓘ |
| coAuthorWith |
Heinz Hopf
ⓘ
Witold Hurewicz ⓘ |
| contribution |
helped shape the modern development of topology
ⓘ
influenced the teaching of topology ⓘ |
| field |
mathematics
ⓘ
topology ⓘ |
| genre | textbook ⓘ |
| hasMathematicalSubjectClassification |
54-01 (expository works in general topology)
ⓘ
55-01 (expository works in algebraic topology) ⓘ |
| influencedBy | early 20th‑century developments in topology ⓘ |
| language | German ⓘ |
| namedAfter | the mathematical field of topology ⓘ |
| notableFor | systematic presentation of early 20th‑century topology ⓘ |
| pedagogicalRole | standard reference for early courses in topology ⓘ |
| subjectOf | historical discussions of topology textbooks ⓘ |
| topic |
algebraic topology
ⓘ
general topology ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: "Topologie" (with W. Hurewicz) Description of subject: "Topologie" (with W. Hurewicz) is a foundational textbook in topology co-authored by Heinz Hopf and Witold Hurewicz that helped shape the modern development and teaching of the subject.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.