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  "body": "\n## Summary\n\nFor a locally compact Hausdorff space $X$, the space $C_0(X)$ consists of the continuous functions that become small outside compact sets.\nIt is a closed subspace of the [[space of bounded continuous functions|MG3X8Y1VT4]], so it is a Banach space with the supremum norm.\nBy the Riesz–Markov–Kakutani theorem, its dual is the space of finite signed regular Borel measures on $X$, or complex ones for complex scalars.\nIt is also the basic example of a commutative C*-algebra without unit.\n\n## Explanations\n\n### L1 human\n\nA function vanishes at infinity when it gets as small as you like once you go far enough away.\nOn $\\R$, the bell curve $e^{-x^2}$ vanishes at infinity, and so does $1/(1 + x^2)$.\nThe constant function $1$ does not.\nOn the set $\\N$ of natural numbers, these functions are just the sequences that tend to $0$.\n",
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