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Some trait cleanup for Sphere S169 (#1799)
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spaces/S000169/properties/P000016.md

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value: true
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This space is a closed and bounded subspace of the Euclidean space $\mathbb{R}^3$.
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This space is a closed and bounded subspace of the Euclidean space $\mathbb{R}^3$.

spaces/S000169/properties/P000086.md

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spaces/S000169/properties/P000137.md

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spaces/S000169/properties/P000199.md

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- zb: "1044.55001"
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name: Algebraic Topology (Hatcher)
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This is a consequence of Corollary 2.14 and the statement after Corollary 2.11 of {{zb:1044.55001}}.

spaces/S000169/properties/P000240.md

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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}.
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See Example 0.3 in {{zb:1044.55001}}.
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See Example 0.3 in {{zb:1044.55001}}.

spaces/S000170/properties/P000240.md

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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 $f_1(\pm 1) = *$.)
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See Example 0.3 in {{zb:1044.55001}}.
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See Example 0.3 in {{zb:1044.55001}}.

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