= Manifold boundary
{title2=$\partial M$}
= Boundary of a topological manifold
{synonym}
The manifold boundary of a <topological manifold with boundary> consists of the points which, in a half-space <coordinate chart>, have last coordinate zero. These are precisely the points without a <neighbourhood> <homeomorphic> to an <open set> in the full <Euclidean space> of the same dimension. It is an intrinsic property, independent of the <coordinate chart>. It differs from the <boundary of a set> in an ambient <topological space>: a <circle> has empty manifold boundary, but its <boundary of a set> in the <Euclidean plane> is the entire <circle>.
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