Boundary (of a manifold)

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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.



[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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098