several easy homogeneous results

spaces/S000015/properties/P000086.md

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+---
+space: S000015
+property: P000086
+value: true
+---
+
+Follows by construction.

spaces/S000017/properties/P000086.md

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+---
+space: S000017
+property: P000086
+value: true
+---
+
+Follows by construction.

spaces/S000018/properties/P000086.md

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+---
+space: S000018
+property: P000086
+value: true
+---
+
+Follows as it is the product of {P86} spaces.

spaces/S000019/properties/P000086.md

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+---
+space: S000019
+property: P000086
+value: true
+---
+
+Follows by construction (since {S25} is).

spaces/S000038/properties/P000086.md

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+---
+space: S000038
+property: P000086
+value: false
+---
+
+Every point except $\langle 0,0 \rangle$ is a cut point, and $\langle 0,0 \rangle$ is not.

spaces/S000039/properties/P000086.md

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+---
+space: S000039
+property: P000086
+value: false
+---
+
+Follows as $\langle 1,0 \rangle$ is a cut point but $\langle 0,0 \rangle$ is not.
+Alternatively, $\langle \omega_1,0 \rangle$ is the unique point at which the space
+is not {P28}.

spaces/S000040/properties/P000086.md

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+---
+space: S000040
+property: P000086
+value: false
+---
+
+Follows as $\langle 1,0 \rangle$ is a cut point but $\langle 0,0 \rangle$ is not.
+Alternatively, $\infty$ is the unique point at which the space
+is not {P28}.

spaces/S000041/properties/P000086.md

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+---
+space: S000041
+property: P000086
+value: false
+---
+
+Follows as $\langle 0,1 \rangle$ is a cut point but $\langle 0,0 \rangle$ is not.

spaces/S000042/properties/P000086.md

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+---
+space: S000042
+property: P000086
+value: true
+---
+
+Follows by construction.

spaces/S000044/properties/P000086.md

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+---
+space: S000044
+property: P000086
+value: false
+---
+
+$1$ is a closed point, but $1/3$ is not.

spaces/S000045/properties/P000086.md

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+---
+space: S000045
+property: P000086
+value: false
+---
+
+$0$ belongs to every nonempty open set, but $1$ does not.