Cell-attachment support dependency map
This map shows the container's direct articles. Nested containers are collapsed and clickable; dependency edges are rolled up from their leaves. fully proved48Proved, and every prerequisite is fully proved too.
graph LR
n0["Every abstract cell attachment has an indexed cone model"]:::fully_proved
n1["Hatcher's auxiliary cell-attachment cover<br/><small>9 items · 9 fully proved</small>"]:::scope
n2["A binary cover with a contractible second piece"]:::fully_proved
n3["A binary cover with a trivial second fundamental group"]:::fully_proved
n4("The degree-n circle map sends the generator to the degree-n loop"):::fully_proved
n5("The circle is well-pointed at one"):::fully_proved
n6["The cone on a disk boundary is the disk"]:::fully_proved
n7["The degree-n circle relation gives the cyclic group"]:::fully_proved
n8["The boundary of the two-disk is the circle"]:::fully_proved
n9["An attachment with no cells is an isomorphism"]:::fully_proved
n10("Higher-cell attachments preserve path components"):::fully_proved
n11["An indexed cone attachment is a standard cell attachment"]:::fully_proved
n12("An indexed family of cones has a two-set open cover"):::fully_proved
n13("An indexed family of cone attachments is a topological pushout"):::fully_proved
n14("The 2-skeleton of a path-connected CW complex is path-connected"):::fully_proved
n15["A single cone attachment is a standard cell attachment"]:::fully_proved
n16["The base-side cone cover retracts onto the original space"]:::fully_proved
n17["The single-cone cover intersection has the homotopy type of its boundary"]:::fully_proved
n18("A single cone attachment has a two-set open cover"):::fully_proved
n19("A single cone attachment is a topological pushout"):::fully_proved
n20("The cone-side cover member is contractible"):::fully_proved
n21["External chapter: Appendix<br/><small>2 items · 2 fully proved</small>"]:::boundary
n22["External chapter: The fundamental group<br/><small>14 items · 14 fully proved</small>"]:::boundary
n23["External chapter: Homology<br/><small>3 items · 3 fully proved</small>"]:::boundary
n21 -. 2 .-> n14
n22 -. 2 .-> n2
n22 -.-> n3
n22 --> n4
n22 --> n7
n22 --> n8
n22 -.-> n1
n0 --> n22
n0 --> n9
n0 -.-> n10
n0 --> n1
n2 -.-> n22
n3 --> n22
n4 --> n22
n5 --> n22
n6 --> n22
n6 --> n11
n6 --> n15
n7 --> n22
n8 -->|3| n22
n8 --> n1
n9 --> n22
n9 -.-> n22
n9 -.-> n10
n10 -.-> n22
n10 -.-> n14
n11 -->|4| n22
n11 --> n0
n12 --> n22
n12 --> n9
n12 -.-> n10
n12 --> n13
n12 --> n1
n13 --> n11
n14 -.-> n22
n16 -.-> n23
n16 -.-> n1
n17 -.-> n23
n17 -.-> n1
n18 --> n22
n18 --> n23
n18 --> n6
n18 --> n12
n18 --> n16
n18 --> n17
n18 --> n19
n18 --> n20
n19 -.-> n23
n19 --> n15
n20 -.-> n23
n20 -.-> n1
n1 -->|3| n22
n1 -. 8 .-> n22
n1 -.-> n10
click n0 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#abstract-cell-attachment-indexed-model" "Every abstract cell attachment has an indexed cone model — 1 item · 1 fully proved"
click n1 "cell-attachment-support/auxiliary.html" "Hatcher's auxiliary cell-attachment cover — 9 items · 9 fully proved"
click n2 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#binary-cover-contractible-piece" "A binary cover with a contractible second piece — 1 item · 1 fully proved"
click n3 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#binary-cover-trivial-piece-quotient" "A binary cover with a trivial second fundamental group — 1 item · 1 fully proved"
click n4 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#circle-degree-map" "The degree-n circle map sends the generator to the degree-n loop — 1 item · 1 fully proved"
click n5 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#circle-well-pointed" "The circle is well-pointed at one — 1 item · 1 fully proved"
click n6 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#cone-disk-homeomorphism" "The cone on a disk boundary is the disk — 1 item · 1 fully proved"
click n7 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#cyclic-relation-quotient" "The degree-n circle relation gives the cyclic group — 1 item · 1 fully proved"
click n8 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#disk-boundary-two-circle" "The boundary of the two-disk is the circle — 1 item · 1 fully proved"
click n9 "../../../../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 n10 "../../../../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 n11 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#indexed-basic-cell-attachment" "An indexed cone attachment is a standard cell attachment — 1 item · 1 fully proved"
click n12 "../../../../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 n13 "../../../../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 n14 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#path-connected-two-skeleton" "The 2-skeleton of a path-connected CW complex is path-connected — 1 item · 1 fully proved"
click n15 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#single-basic-cell-attachment" "A single cone attachment is a standard cell attachment — 1 item · 1 fully proved"
click n16 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#single-cone-base-retract" "The base-side cone cover retracts onto the original space — 1 item · 1 fully proved"
click n17 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#single-cone-intersection" "The single-cone cover intersection has the homotopy type of its boundary — 1 item · 1 fully proved"
click n18 "../../../../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"
click n19 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#single-cone-pushout" "A single cone attachment is a topological pushout — 1 item · 1 fully proved"
click n20 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#single-cone-upper-contractible" "The cone-side cover member is contractible — 1 item · 1 fully proved"
click n21 "../../../chapters/appendix.html" "Appendix — 2 items · 2 fully proved"
click n22 "../../../chapters/fundamental-group.html" "The fundamental group — 14 items · 14 fully proved"
click n23 "../../../chapters/homology.html" "Homology — 3 items · 3 fully proved"