Local degree is independent of its 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 proved3Proved, and every prerequisite is fully proved too.ready to state1Prerequisites are stated, so this can be written down.

graph LR n0("Local degree is unchanged when the neighborhood shrinks"):::fully_proved n1("Local degree is independent of its neighborhood"):::fully_proved n2("The finite-fiber pair map acts by the local degrees"):::fully_proved n3("A local homeomorphism has local degree plus or minus one"):::can_state n0 --> n1 n1 --> n2 n1 --> n3 click n0 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#local-degree-shrinking" "Local degree is unchanged when the neighborhood shrinks — 1 item · 1 fully proved" class n1 focus click n1 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#local-degree-well-defined" "Local degree is independent of its neighborhood — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#finite-fiber-local-map" "The finite-fiber pair map acts by the local degrees — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#homeomorphism-local-degree" "A local homeomorphism has local degree plus or minus one — 1 item · 1 ready to state"