「被覆空間」の版間の差分

Covering spaces play an important role in [[homotopy theory]], [[harmonic analysis]], [[Riemannian geometry]] and [[differential topology]]. In Riemannian geometry for example, [[Ramification#In algebraic topology|ramification]] is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the [[fundamental group]]. An important application comes from the result that, if ''X'' is a "sufficiently good" [[topological space]], there is a [[bijection]] from the collection of all isomorphism classes of [[connected space|connected coverings]] of ''X'' and subgroups of the [[fundamental group]] of ''X''.-->

 

X を[[位相空間]]とする。X の'''被覆空間'''とは、位相空間 C および[[連続函数|連続]][[全射]]

:<math>p : C \rightarrow X</math>