A finite sphere-map fiber has disjoint isolated neighborhoods: 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 proved4Proved, and every prerequisite is fully proved too.

graph LR n0["An isolated preimage gives a map of punctured pairs"]:::fully_proved n1["A finite sphere-map fiber has disjoint isolated neighborhoods"]:::fully_proved n2("The disjoint local pairs excise to the finite-puncture pair"):::fully_proved n3("The finite-fiber pair map carries the global degree"):::fully_proved n1 --> n2 n1 --> n3 n0 --> n1 click n0 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#isolated-preimage-neighborhood" "An isolated preimage gives a map of punctured pairs — 1 item · 1 fully proved" class n1 focus click n1 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#finite-fiber-neighborhoods" "A finite sphere-map fiber has disjoint isolated neighborhoods — 1 item · 1 fully proved" click n2 "../../../../../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" click n3 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#global-degree-fiber-square" "The finite-fiber pair map carries the global degree — 1 item · 1 fully proved"