An indexed family of cones has a two-set open cover: 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. fully proved7Proved, and every prerequisite is fully proved too.
graph LR
n0("A single cone attachment has a two-set open cover"):::fully_proved
n1("An indexed family of cones has a two-set open cover"):::fully_proved
n2("An indexed family of cone attachments is a topological pushout"):::fully_proved
n3["The strip-enlarged cell-attachment space"]:::fully_proved
n4["An attachment with no cells is an isomorphism"]:::fully_proved
n5("Higher-cell attachments preserve path components"):::fully_proved
n6["The cyclic presentation complex"]:::fully_proved
n4 -.-> n5
n1 --> n3
n1 --> n4
n1 -.-> n5
n1 --> n2
n1 --> n6
n0 --> n1
click n0 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#single-cone-open-cover" "A single cone attachment has a two-set open cover — 1 item · 1 fully proved"
class n1 focus
click n1 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#indexed-cone-open-cover" "An indexed family of cones has a two-set open cover — 1 item · 1 fully proved"
click n2 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#indexed-cone-pushout" "An indexed family of cone attachments is a topological pushout — 1 item · 1 fully proved"
click n3 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-cell-attachment-space" "The strip-enlarged cell-attachment space — 1 item · 1 fully proved"
click n4 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#empty-cell-attachment-iso" "An attachment with no cells is an isomorphism — 1 item · 1 fully proved"
click n5 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#higher-cell-attachment-path-components" "Higher-cell attachments preserve path components — 1 item · 1 fully proved"
click n6 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#cyclic-presentation-complex" "The cyclic presentation complex — 1 item · 1 fully proved"