Geodesic
Connection homology and cohomology between sets. Enclosure homology and cohomology of a closed set
Izvestiya. Mathematics , Tome 41 (1993) no. 2, pp. 307-335

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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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     author = {E. G. Sklyarenko},
     title = {Connection homology and cohomology between sets. {Enclosure} homology and cohomology of a closed set},
     journal = {Izvestiya. Mathematics },
     pages = {307--335},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1993_41_2_a6/}
}
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E. G. Sklyarenko. Connection homology and cohomology between sets. Enclosure homology and cohomology of a closed set. Izvestiya. Mathematics , Tome 41 (1993) no. 2, pp. 307-335. http://geodesic.mathdoc.fr/item/IM2_1993_41_2_a6/