Naslov
Steenrod-Sitnikov homology for arbitrary spaces

Autori
Lisica , Ju. T. ; Mardešić, Sibe

Izvornik
Bulletin of the american mathematical society (0273-0979) 9 (1983); 207-219

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Steenrod-Sitnikov homology theory for arbitrary topological spaces ; strong homology of inverse systems ; ANR-resolutions ; strong shape category

Sažetak
In 1940 N. E. Steenrod introduced a new type of homology for metric compacta in order to obtain an Alexander duality theorem for compact subsets of Sn. In 1951 K. A. Sitnikov was led by the same problem to an equivalent theory. Then in 1960 J. Milnor gave an axiomatic characterization of the Steenrod-Sitnikov homology theory. Various authors later extended the theory to the compact Hausdorff case. The purpose of this announcement is to define a Steenrod-Sitnikov homology theory for arbitrary topological spaces. The authors refer to it as strong homology. It is obtained by developing strong homology of inverse systems. The transition from spaces to systems is achieved by means of ANR-resolutions. The latter is a generalization (due to the second author) of inverse systems which is more appropriate in the case of noncompact spaces. Strong homology groups of a space are then defined as strong homology groups of any of its ANR-resolutions. As a consequence of this approach the authors get that strong homology is a functor on the strong shape category.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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