{
  "id": "1701.00356",
  "version": "v1",
  "published": "2017-01-02T10:27:27.000Z",
  "updated": "2017-01-02T10:27:27.000Z",
  "title": "On spaces with $σ$-closed discrete dense sets",
  "authors": [
    "Rodrigo R. Dias",
    "Daniel T. Soukup"
  ],
  "comment": "16 pages, first public version",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "The main purpose of this paper is to study $e$-separable spaces, originally introduced by Kurepa as $K_0'$ spaces; a space $X$ is $e$-separable iff $X$ has a dense set which is the union of countably many closed discrete sets. We primarily focus on the behaviour of $e$-separable spaces under products and the cardinal invariants that are naturally related to $e$-separable spaces. Our main results show that the statement \"the product of at most $\\mathfrak c$ many $e$-separable spaces is $e$-separable\" depends on the existence of certain large cardinals and hence independent of ZFC.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-02T10:27:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D65",
      "54A25",
      "54A35"
    ],
    "keywords": [
      "closed discrete dense sets",
      "separable spaces",
      "main purpose",
      "closed discrete sets",
      "large cardinals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}