A manifold without boundary of dimension 
is a topological space
that is a T2-space, has a second
countable topology, and is locally Euclidean
of dimension 
. Thus every point has an open
neighborhood homeomorphic to an open
set in 
,
where 
is a fixed nonnegative integer (Lee 2013,
p. 3).
A manifold without boundary is called a closed manifold when it is compact and an open manifold when it is noncompact (Lee 2013, p. 27). For example, the circle is a closed manifold, whereas the real line is an open manifold.
A manifold with boundary is a manifold without boundary iff its manifold boundary is empty (Lee 2013, p. 27). This is the intrinsic manifold boundary, rather than the boundary of a subset of a chosen ambient topological space.
