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  "body": "\n## Summary\n\nAlexander–Spanier cohomology is a cohomology theory for topological spaces built from arbitrary functions on tuples of points, taken modulo functions that vanish near the diagonal.\nIt does not use simplices or maps from a model space, so it behaves well on spaces with bad local structure.\nOn paracompact Hausdorff spaces it agrees with Čech cohomology and with sheaf cohomology of a constant sheaf.\nOn manifolds and CW complexes it agrees with [[singular cohomology|6N7BC70CX0]].\n\n## Explanations\n\n### L1 human\n\nSingular cohomology probes a space with maps of triangles into it.\nOn wild spaces such maps may miss features that you can see by eye.\nAlexander–Spanier cohomology instead looks at functions of several points that only matter when the points are close together.\nFor example, the Warsaw circle is a circle with a wild oscillating piece.\nIt has no first singular cohomology, but its Alexander–Spanier cohomology sees the loop, as it does for an ordinary circle.\n",
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