A locally Euclidean topological space of dimension 
is a space in which every point
has an open neighborhood homeomorphic
to an open set in 
, where 
is a fixed nonnegative
integer (Lee 2013, p. 3). The T2-space
and second countable topology conditions
required of a manifold without boundary
are additional hypotheses.
For a local group, Goldbring (2010, p. 1271) uses locally Euclidean to require this condition only at the identity element. For a topological group, the condition at the identity element implies the condition at every point by translation.
