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Includes reference to the definition
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spaces/S000106/README.md

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name: Answer to "Is the weak topology on $\mathbb{R}^{\infty}$ the same as the box topology?"
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- mathse: 5012784
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name: Answer to "Is $\ell^\infty$ with box topology connected?"
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- zb: "0298.57008"
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name: Characteristic classes (Milnor-Stasheff)
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- zb: "0307.55015"
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name: Fibre bundles. 2nd ed. (Husemoller)
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- zb: "1280.54001"
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name: Geometric aspects of general topology. (Sakai)
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- wikipedia: Fréchet–Urysohn_space
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name: Fréchet–Urysohn space on Wikipedia
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---
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The subset $\mathbb{R}^\infty$ of eventually $0$ sequences in $\mathbb{R}^\omega$, with the finest
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topology such that the standard inclusion maps $\mathbb{R}^n \hookrightarrow \mathbb{R}^\infty$,
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as a path component.
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For general discussion on direct limits, see {{wikipedia:Direct_limit}}.
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Defined on page 62 of {{zb:"0298.57008"}}, on page 2 of {{zb:"0307.55015"}},
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on page 56 of {{zb:"1280.54001}}, and on {{wikipedia:Fréchet–Urysohn_space}}
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under Direct limit of finite-dimensional Euclidean spaces.

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