discrete and codiscrete topology
Discrete and concrete objects
The forgetful functor from Top to Set that sends any topological space to its underlying set has a left adjoint and a right adjoint .
is the topological space on in which every subset is an open set
this is called the discrete topology on , is called a discrete space;
is the topological space on whose only open sets are the empty set and itself
this is called the codiscrete topology on (also indiscrete topology or trivial topology), is called a codiscrete space .
For an axiomatization of this situation see codiscrete object.
Revised on October 11, 2012 11:50:08
by Urs Schreiber