= Borel-Moore homology
{c}
{title2=$H_*^{\rm BM}(X)$}
= Locally finite homology
{synonym}
For a locally compact space, replace finite <singular chains> by chains for which every compact subset meets the images of only finitely many simplices with nonzero coefficients. The <boundary operator> preserves this local finiteness, giving the Borel-Moore chain complex and its <homology>. On a compact space it reduces to ordinary singular homology. A noncompact manifold has a locally finite <fundamental class>, with its <orientation local system> when necessary. The chain groups and homology are zero in negative degrees.
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