nLab
boundary

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Definition

Of a subset of a topological space

For S⊂X a subset of a topological space X, the boundary or frontier ∂S of S is its closure S¯ minus its interior S ∘:

∂S=S¯\S ∘\partial S = \bar S \backslash S^\circ

Of a manifold

In a manifold with boundary of dimension n the boundary is the collection of points which do not have a neighborhood diffeomorphic to an open n-ball, but do have a neighborhood homeomorphic to a half-ball, that is, an open ball intersected with closed half-space.

H n=Z n/B n(chain-)homology(cochain-)cohomologyH n=Z n/B n
C nchaincochainC n
Z n⊂C ncyclecocycleZ n⊂C n
B n⊂C nboundarycoboundaryB n⊂C n

Revised on April 27, 2013 13:04:38 by Urs Schreiber (89.204.139.246)
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