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  "body": "\n## Statement\n\nLet $X$ be a [[compact space|0QPHW703PV]]. Let $C(X)$ be the [[space of bounded continuous functions|D38YWGXRKJ]] on $X$, which is a [[Banach space|06GZ956657]] under the supremum norm.\n\nA Banach space $E$ is *Asplund* when each closed separable subspace of $E$ has a separable [[continuous dual space|4A82S5FVRT]].\n\nThe space $X$ is *scattered* when each nonempty subset $A \\subseteq X$ has a point that is [[isolated|01PKQYTTMT]] in $A$ for the subspace topology.\n\nThen $C(X)$ is Asplund if and only if $X$ is scattered.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
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      "notes": "The source is arXiv:2510.01873v1 (2025-10), by Marian Fabian, Jerzy Kcakol, Arkady Leiderman. A paper also restates older results, so this is not the first statement until a person or a later pass confirms it."
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      {
        "arxiv": "2510.01873v1",
        "licence": "cc-by",
        "locator": "Theorem 2.5",
        "mention": "ax://paper/2510.01873#5CZ6",
        "note": "the paper that states the item (corpus arxiv AX9.2)"
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  "name": "Namioka--Phelps",
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