functor of continuous functions

 topology
Notation C:Topop→CAlg(R)C: \Top^{\op} \to \CAlg(R) Domain dual of the category of topological spacesCodomain category of commutative algebras
This functor maps a topological space XX to the commutative R\IR-algebra C(X)C(X) of continuous functions X→RX \to \IR. A continuous map f:X→Yf : X \to Y is mapped to the algebra homomorphism f∗:C(Y)→C(X)f^* : C(Y) \to C(X), u↦u∘fu \mapsto u \circ f.

Satisfied properties

Assigned properties

Deduced properties

Unsatisfied properties

Assigned properties

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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