J. Munkres, Elementary Differential Topology
E288084
"J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| J. Munkres, Elementary Differential Topology canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2652956 — 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: J. Munkres, Elementary Differential Topology Context triple: [Whitney approximation theorem, standardReference, J. Munkres, Elementary Differential Topology]
-
A.
M. Hirsch, Differential Topology
*Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
-
B.
J. Lee, Introduction to Smooth Manifolds
*J. Lee, Introduction to Smooth Manifolds* is a widely used graduate-level textbook that provides a rigorous and accessible introduction to the theory of smooth manifolds and differential topology.
-
C.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
-
D.
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.
-
E.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
- 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: J. Munkres, Elementary Differential Topology Target entity description: "J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
-
A.
M. Hirsch, Differential Topology
*Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
-
B.
J. Lee, Introduction to Smooth Manifolds
*J. Lee, Introduction to Smooth Manifolds* is a widely used graduate-level textbook that provides a rigorous and accessible introduction to the theory of smooth manifolds and differential topology.
-
C.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
-
D.
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.
-
E.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
- F. None of above. chosen
Statements (34)
| Predicate | Object |
|---|---|
| instanceOf |
differential topology textbook
ⓘ
mathematics book ⓘ textbook ⓘ |
| approach |
introductory
ⓘ
rigorous ⓘ |
| author | James R. Munkres ⓘ |
| field |
differential topology
ⓘ
topology ⓘ |
| hasReputation | classic text in differential topology ⓘ |
| language | English ⓘ |
| pedagogicalLevel |
advanced undergraduate
ⓘ
beginning graduate ⓘ |
| topic |
Sard’s theorem
ⓘ
linked to:
Sard's theorem
applications of Sard’s theorem ⓘ approximation theorems ⓘ degree of a map ⓘ differentiable maps ⓘ differential forms ⓘ embeddings ⓘ flows ⓘ homotopy of maps ⓘ immersions ⓘ integration on manifolds ⓘ isotopy ⓘ orientation of manifolds ⓘ partitions of unity ⓘ regular values ⓘ smooth manifolds ⓘ submanifolds ⓘ submersions ⓘ tangent spaces ⓘ transversality ⓘ vector fields ⓘ |
| usedAs | university course textbook ⓘ |
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: J. Munkres, Elementary Differential Topology Description of subject: "J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.