{
  "id": "1712.08540",
  "version": "v1",
  "published": "2017-12-22T16:04:13.000Z",
  "updated": "2017-12-22T16:04:13.000Z",
  "title": "On closed non-vanishing ideals in CB(X)",
  "authors": [
    "A. Khademi",
    "M. R. Koushesh"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a completely regular topological space. We study closed ideals $H$ of $C_B(X)$, the normed algebra of bounded continuous scalar-valued mappings on $X$ equipped with pointwise addition and multiplication and the supremum norm, which are non-vanishing, in the sense that, there is no point of $X$ at which every element of $H$ vanishes. This is done by studying the (unique) locally compact Hausdorff space $Y$ associated to $H$ in such a way that $H$ and $C_0(Y)$ are isometrically isomorphic. We are interested in various connectedness properties of $Y$. In particular, we present necessary and sufficient (algebraic) conditions for $H$ such that $Y$ satisfies (topological) properties such as locally connectedness, total disconnectedness, zero-dimensionality, strong zero-dimensionality, total separatedness or extremal disconnectedness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-22T16:04:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "closed non-vanishing ideals",
      "locally compact hausdorff space",
      "strong zero-dimensionality",
      "study closed ideals",
      "total disconnectedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}