# 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). M.I. Voitsekhovskii (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Boundary_(of_a_manifold)&oldid=14973

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098