{
  "id": "2012.13439",
  "version": "v1",
  "published": "2020-12-24T20:33:23.000Z",
  "updated": "2020-12-24T20:33:23.000Z",
  "title": "Szlenk index of $C(K)\\widehat{\\otimes}_πC(L)$",
  "authors": [
    "R. M. Causey",
    "E. Galego",
    "C. Samuel"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We compute the Szlenk index of an arbitrary projective tensor product $C(K)\\widehat{\\otimes}_\\pi C(L)$ of spaces $C(K), C(L)$ of continuous functions on scattered, compact, Hausdorff spaces. In particular, we show that it is simply equal to the maximum of the Szlenk indices of the spaces $C(K), C(L)$. We deduce several results regarding non-isomorphism of $C(K)\\widehat{\\otimes}_\\pi C(L)$ and $C(M)$ or $C(M)\\widehat{\\otimes}_\\pi C(N)$ for particular choices of $K,L,M,N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-24T20:33:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "szlenk index",
      "arbitrary projective tensor product",
      "hausdorff spaces",
      "results regarding non-isomorphism",
      "continuous functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}