Connection homology and cohomology between sets. Enclosure homology and cohomology of a closed set

E. G. Sklyarenko

Izvestiya. Mathematics , Tome 41 (1993) no. 2, pp. 307-335.

Résumé

The notions of connection homology and cohomology between complementary subsets of a topological space are defined, using passage to the limit with respect to boundary-open sets, i.e., complements of pairs of closed subsets of the given complementary sets. The homology and cohomology groups so obtained enter naturally into new exact homology and cohomology sequences.

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