# nLab Steenrod-Sitnikov homology

In order to establish an Alexander duality theorem for compact subsets of $S^n$, Steenrod introduced in 1940 a new type of homology of metric compacta; a summary of the construction is given in the entry, Steenrod homology. The same problem led K. A. Sitnikov in 1951 to an equivalent theory and in 1960 J. Milnor gave an axiomatic characterization of the resulting ‘Steenrod-Sitnikov homology’.

Several authors extended this to compact Hausdorff spaces and then Lisica and Mardešić gave a definition for arbitrary spaces.

## References

• Ju. T. Lisica and S. Mardešić, Steenrod–Sitnikov homology for arbitrary spaces, Bull. Amer. Math. Soc. 9 (1983), 207–210.

• S. Mardešić, Strong shape and homology, Springer monographs in mathematics, 2000. xii+489 pp.

Last revised on July 25, 2018 at 11:44:05. See the history of this page for a list of all contributions to it.