View source for Boundary (of a manifold)

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The subset of the closure  $  \overline{ {M  ^ {n} }}\; $
of an (open)  $  n $-
dimensional real manifold  $  M  ^ {n} $
for which a neighbourhood of each point is homeomorphic to some domain  $  W  ^ {n} $
in the closed half-space of  $  \mathbf R  ^ {n} $, 
the domain being open in  $  \mathbf R _ {+}  ^ {n} $(
but not in  $  \mathbf R  ^ {n} $). 
A point  $  a \in \overline{ {M  ^ {n} }}\; $
corresponding to a boundary point of  $  W  ^ {n} \subset  \mathbf R _ {+}  ^ {n} $, 
i.e. to an intersection point of  $  \overline{ {W  ^ {n} }}\; $
with the boundary of  $  \mathbf R _ {+}  ^ {n} $, 
is called a boundary point of  $  M  ^ {n} $. 
A manifold having boundary points is known as a manifold with boundary. A compact manifold without boundary is known as a closed manifold. The set of all boundary points of  $  M  ^ {n} $
is an  $  (n - 1) $-
dimensional manifold without boundary.

====Comments====

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M.W. Hirsch,   "Differential topology" , Springer  (1976)</TD></TR></table>