Circle and Sphere are CW complexes (#1797)

Author: artemetra

spaces/S000169/properties/P000240.md

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+---
+space: S000169
+property: P000240
+value: true
+refs:
+  - zb: "1044.55001"
+    name: Algebraic Topology (Hatcher)
+  - wikipedia: Suspension_(topology)
+    name: Suspension on Wikipedia
+---
+
+
+The circle can be given a CW complex structure by associating one $0$-cell and one $2$-cell: Start with $X_0=\{*\}$, then attach a $2$-cell $D^2$ by identifying the boundary $\partial D^2$ with the $0$-cell (define $f_2: \partial D^2 \to X_0$ by $f_2(\partial D^2) = *$.)
+
+Equivalently, this follows from the fact that CW complexes are preserved under suspensions, and since the sphere is a suspension of {S170}, which is a CW complex {S170|P240}.
+
+See Example 0.3 in {{zb:1044.55001}}.

spaces/S000170/properties/P000240.md

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+---
+space: S000170
+property: P000240
+value: true
+refs:
+  - zb: "1044.55001"
+    name: Algebraic Topology (Hatcher)
+---
+
+The circle can be given a CW complex structure by associating one $0$-cell and one $1$-cell: Start with $X_0=\{*\}$, then attach a $1$-cell $D^1 = [-1,1]$ by identifying both boundary points with the $0$-cell (define $f_1: \partial D^1 \to X_0$ by $f_1(\pm 1) = *$.)
+
+See Example 0.3 in {{zb:1044.55001}}.