The presheaf of continuous functions on X with values in fixed target topological space T.

The (bundled) commutative ring of continuous functions from a topological space to a topological commutative ring, with pointwise multiplication.

Pulling back functions into a topological ring along a continuous map is a ring homomorphism.

A homomorphism of topological rings can be postcomposed with functions from a source space X; this is a ring homomorphism (with respect to the pointwise ring operations on functions).

An upgraded version of the Yoneda embedding, observing that the continuous maps from X : Top to R : TopCommRing form a commutative ring, functorial in both X and R.

The presheaf (of commutative rings), consisting of functions on an open set U ⊆ X with values in some topological commutative ring T.

The presheaf (of commutative rings) of real valued functions.

The presheaf (of commutative rings) of complex valued functions.