Homology of a point: 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

in mathlib3Upstreamed into Mathlib.fully proved3Proved, and every prerequisite is fully proved too.

graph LR n0["Singular homology"]:::mathlib n1["Zeroth homology is free on path components"]:::mathlib n2("Higher homology vanishes for totally disconnected spaces"):::mathlib n3("Homology of a point"):::fully_proved n4["Relative homology at a basepoint is reduced homology"]:::fully_proved n5("The identity simplex generates relative simplex homology"):::fully_proved n3 -.-> n5 n3 -.-> n4 n0 --> n3 n0 --> n2 n0 --> n1 n2 -.-> n3 n1 -.-> n3 click n0 "../../../../roadmap/homology/simplicial-and-singular/index.html#singular-homology" "Singular homology — 1 item · 1 in mathlib" click n1 "../../../../roadmap/homology/simplicial-and-singular/index.html#zeroth-homology-components" "Zeroth homology is free on path components — 1 item · 1 in mathlib" click n2 "../../../../roadmap/homology/simplicial-and-singular/index.html#totally-disconnected-higher-homology" "Higher homology vanishes for totally disconnected spaces — 1 item · 1 in mathlib" class n3 focus click n3 "../../../../roadmap/homology/simplicial-and-singular/index.html#point-homology" "Homology of a point — 1 item · 1 fully proved" click n4 "../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#pointed-relative-reduced-homology" "Relative homology at a basepoint is reduced homology — 1 item · 1 fully proved" click n5 "../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#relative-simplex-fundamental-class" "The identity simplex generates relative simplex homology — 1 item · 1 fully proved"