High Quality Content by WIKIPEDIA articles! In mathematics, particularly in algebraic topology, Alexander–Spanier cohomology is a cohomology theory for topological spaces, introduced by J. W. Alexander (1935) for the special case of compact metric spaces, and by E. H. Spanier (1948) for all topological spaces, based on a suggestion of A. D. Wallace. It is also possible to define Alexander–Spanier homology (Massey 1978) and Alexander–Spanier cohomology with compact supports (Bredon 1997). The Alexander–Spanier cohomology groups coincide with Cech cohomology groups for compact Hausdorff spaces, and coincide with singular cohomology groups for locally finite complexes.

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