Category of topological spaces

The category of topological spaces $𝖳 𝗈 𝗉$ is the category where each object is a topological space and each morphism is a continuous map. #m/def/topology

Well defined category

Composition of continuous maps yields a continuous map
The identity is always continuous
Function composition is already associative

Properties

Universal constructions

The initial object of $𝖳 𝗈 𝗉$ is $\emptyset$ with the unique topology
The terminal object of $𝖳 𝗈 𝗉$ is ${*}$ with the unique topology

Morphisms

Regular monomorphisms in $𝖳 𝗈 𝗉$

$𝖳 𝗈 𝗉 / ≃$ is the Quotient category of $𝗁 𝖳 𝗈 𝗉$ with Homotopy of continuous maps.

#state/develop | #lang/en | #SemBr