Deleted-pair homology is local on an open neighborhood: local context

Project map · Chapter map · Full theorem DAG · Open textbook statement

This local map shows one dependency hop in either direction. The highlighted item is the current focus. What the colours mean

fully proved5Proved, and every prerequisite is fully proved too.

graph LR n0["Relative singular chains and homology"]:::fully_proved n1["Binary-cover excision induces homology isomorphisms"]:::fully_proved n2("Local homology is unchanged on an open neighborhood"):::fully_proved n3("Deleted-pair homology is local on an open neighborhood"):::fully_proved n4("The disjoint local pairs excise to the finite-puncture pair"):::fully_proved n3 --> n4 n2 --> n3 n0 --> n3 n0 --> n2 n0 --> n1 n1 -.-> n3 click n0 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#relative-singular-homology" "Relative singular chains and homology — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#binary-cover-excision-homology-isomorphism" "Binary-cover excision induces homology isomorphisms — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/computations-and-applications/local-homology-and-dimension/index.html#local-homology-open-neighborhood" "Local homology is unchanged on an open neighborhood — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#deleted-pair-open-neighborhood" "Deleted-pair homology is local on an open neighborhood — 1 item · 1 fully proved" click n4 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#finite-puncture-pair-excision" "The disjoint local pairs excise to the finite-puncture pair — 1 item · 1 fully proved"