Eilenberg–Steenrod axioms

E634843
axiomatic system foundational concept in algebraic topology set of axioms

The Eilenberg–Steenrod axioms are a foundational set of conditions that formally characterize homology theories in algebraic topology.

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Observed surface forms (1)

Surface form Occurrences
Eilenberg–Steenrod axioms of homology 1

Statements (45)

Predicate Object
instanceOf axiomatic system ⓘ
foundational concept in algebraic topology ⓘ
set of axioms ⓘ
appliesTo continuous maps ⓘ
pairs of topological spaces ⓘ
assumes abelian category structure on target ⓘ
characterizes ordinary homology theories ⓘ
singular homology ⓘ
codomain graded abelian groups ⓘ
graded modules ⓘ
contrastedWith extraordinary cohomology theories ⓘ
defines homology theory ⓘ
domain topological spaces ⓘ
ensures Mayer–Vietoris sequence NERFINISHED ⓘ
homotopy invariance of homology ⓘ
uniqueness of ordinary homology theories up to natural isomorphism ⓘ
field algebraic topology ⓘ
homological algebra ⓘ
formalizes properties of classical homology ⓘ
generalizedBy Brown representability theorem NERFINISHED ⓘ
implies homology of a point is concentrated in degree zero ⓘ
homology of disjoint union is direct sum of homologies ⓘ
includes boundary homomorphism ⓘ
long exact sequence of a pair ⓘ
influenced development of modern algebraic topology ⓘ
introducedBy Norman Steenrod NERFINISHED ⓘ
Samuel Eilenberg NERFINISHED ⓘ
language category theory ⓘ
namedAfter Norman Steenrod NERFINISHED ⓘ
Samuel Eilenberg NERFINISHED ⓘ
publication Foundations of Algebraic Topology NERFINISHED ⓘ
publicationYear 1952 ⓘ
relatedTo cohomology theories ⓘ
spectra in stable homotopy theory ⓘ
requires additivity axiom ⓘ
dimension axiom ⓘ
exactness axiom ⓘ
excision axiom ⓘ
functoriality ⓘ
homotopy axiom ⓘ
naturality of homology maps ⓘ
topicOf many graduate textbooks in algebraic topology ⓘ
usedFor defining cellular homology ⓘ
defining simplicial homology ⓘ
defining singular homology ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Samuel Eilenberg → notableWork → Eilenberg–Steenrod axioms ⓘ
Samuel Eilenberg → knownFor → Eilenberg–Steenrod axioms ⓘ
this entity surface form: Eilenberg–Steenrod axioms of homology
Samuel Eilenberg → notableConcept → Eilenberg–Steenrod axioms ⓘ
"Algebraic Topology" → developsConcept → Eilenberg–Steenrod axioms ⓘ
subject surface form: Algebraic Topology