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Add infinite earring #795

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Oct 11, 2024
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18 changes: 18 additions & 0 deletions spaces/S000201/README.md
Original file line number Diff line number Diff line change
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---
uid: S000201
name: Infinite earring
aliases:
- Hawaiian earring
refs:
- wikipedia: Hawaiian_earring
name: Hawaiian earring on Wikipedia
- zb: "0951.54001"
name: Topology (Munkres)
---

The subspace of {S176} defined by
$$X=\bigcup_{n=1}^{\infty}\left\{(x,y)\in\mathbb{R}^2:\left(x-\frac{1}{n}\right)^2+y^2=\left(\frac{1}{n}\right)^2\right\}$$
that is, the union of circles of radius $\frac{1}{n}$ centered at $(\frac{1}{n},0)$ for positive
integers $n$.

Defined as "infinite earring" in section 71 of {{zb:0951.54001}}.
7 changes: 7 additions & 0 deletions spaces/S000201/properties/P000016.md
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---
space: S000201
property: P000016
value: true
---

Holds as a closed and bounded subspace of {S176}.
7 changes: 7 additions & 0 deletions spaces/S000201/properties/P000184.md
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---
space: S000201
property: P000184
value: true
---

Holds by definition.