{
  "id": "1310.0396",
  "version": "v1",
  "published": "2013-10-01T17:10:54.000Z",
  "updated": "2013-10-01T17:10:54.000Z",
  "title": "Tychonoff-like Product Theorems for Local Topological Properties",
  "authors": [
    "Simon Brandhorst",
    "Marcel Erné"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We consider classes T of topological spaces (referred to as T-spaces) that are stable under continuous images and frequently under arbitrary products. A local T-space has for each point a neighborhood base consisting of subsets that are T-spaces in the induced topology. A general necessary and sufficient criterion for a product of topological spaces to be a local T-space in terms of conditions on the factors enables one to establish a broad variety of theorems saying that a product of spaces has a certain local property (like local compactness, local sequential compactness, local \\sigma-compactness, local connectedness etc.) if and only if each factor has that local property, almost all have the corresponding global property, and not too many factors fail a suitable additional condition. Many of the results admit a point-free formulation; a look at sum decompositions into components of spaces with local properties yields product decompositions into indecomposable factors for certain classes of frames like completely distributive lattices or hypercontinuous frames.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-01T17:10:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B10",
      "06B35",
      "54D05",
      "54D30",
      "54D45"
    ],
    "keywords": [
      "local topological properties",
      "tychonoff-like product theorems",
      "local property",
      "local properties yields product decompositions",
      "local t-space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.0396B"
    }
  }
}