Boundary (of a manifold)
From Encyclopedia of Mathematics
The subset of the closure 
of an (open) 
-dimensional real manifold 
for which a neighbourhood of each point is homeomorphic to some domain 
in the closed half-space of 
, the domain being open in 
(but not in 
). A point 
corresponding to a boundary point of 
, i.e. to an intersection point of 
with the boundary of 
, is called a boundary point of 
. 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 
is an 
-dimensional manifold without boundary.
Comments
References
| [a1] | M.W. Hirsch, "Differential topology" , Springer (1976) |
How to Cite This Entry:
Boundary (of a manifold). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boundary_(of_a_manifold)&oldid=14973
Boundary (of a manifold). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boundary_(of_a_manifold)&oldid=14973
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article