Homeomorphic nonempty Euclidean open sets have equal dimension: 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 proved3Proved, and every prerequisite is fully proved too.

graph LR n0("Local homology is unchanged on an open neighborhood"):::fully_proved n1("Local homology of positive-dimensional Euclidean space"):::fully_proved n2("Homeomorphic nonempty Euclidean open sets have equal dimension"):::fully_proved n0 -.-> n2 n0 --> n1 n1 -.-> n2 click n0 "../../../../../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 n1 "../../../../../roadmap/homology/computations-and-applications/local-homology-and-dimension/index.html#punctured-euclidean-local-homology" "Local homology of positive-dimensional Euclidean space — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/computations-and-applications/local-homology-and-dimension/index.html#invariance-of-dimension-open-sets" "Homeomorphic nonempty Euclidean open sets have equal dimension — 1 item · 1 fully proved"