Assertion: sequence | /r/HasProperty | x k
Facets:
Source sentences:
text: A sequence ( x k ) {\displaystyle (x_{k})} in a topological group G {\displaystyle G} is a Cauchy sequence if for every open neighbourhood U {\displaystyle U} of the identity in G {\displaystyle G} there exists some number N {\displaystyle N} such that whenever m , n > N {\displaystyle m,n>N} it follows that x n x m − 1 ∈ U {\displaystyle x_{n}x_{m}^{-1}\in U} .