forgetful functor for topological spaces

 topology  forgetful
Notation UTop:Top→SetU_{\Top}: \Top \to \Set Domain category of topological spacesCodomain category of setsLeft adjoint discrete topology functorRight adjoint indiscrete topology functor Related π0\pi_0 External nLab link
This functor maps a topological space XX to its underlying set UTop(X)U_{\Top}(X).

Satisfied properties

Assigned properties

Deduced properties

Unsatisfied properties

Assigned properties

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

—

Comments

  • This functor has exactly two right inverses (up to isomorphism), see MSE/4368730.