Principal bundle
In the mathematical area of topology, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product X × G {\displaystyle X\times G} of a topological space X {\displaystyle X} with a group G {\displaystyle G} , but without requiring a product structure. In the same way as with the Cartesian product, a principal bundle P {\displaystyle P} is equipped with An action of G {\displaystyle G} on P {\displaystyle P} , analogous to ( x , g ) h = ( x , g h ) {\displaystyle (x,g)h=(x,gh)} for a product space (where ( x , g ) {\displaystyle (x,g)} is an element of P {\displaystyle P} and h {\displaystyle h} is the group element from G {\displaystyle G} ; the group action is conventionally a right action).