Disjoint punctured neighborhoods form the deleted union pair: 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["The coproduct of a family of topological pairs"]:::fully_proved n1("Local homology is unchanged on an open neighborhood"):::fully_proved n2["A disjoint open family is homeomorphic to its sigma type"]:::fully_proved n3["Disjoint punctured neighborhoods form the deleted union pair"]:::fully_proved n4("The disjoint local pairs excise to the finite-puncture pair"):::fully_proved n2 --> n3 n3 --> n4 n0 --> n3 n1 --> n3 click n0 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#sigma-topological-pair" "The coproduct of a family of topological pairs — 1 item · 1 fully proved" click n1 "../../../../../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" click n2 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#disjoint-open-union-homeomorphism" "A disjoint open family is homeomorphic to its sigma type — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#disjoint-punctured-pair-iso" "Disjoint punctured neighborhoods form the deleted union pair — 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"