{
  "id": "1905.00513",
  "version": "v1",
  "published": "2019-05-01T21:54:09.000Z",
  "updated": "2019-05-01T21:54:09.000Z",
  "title": "On $\\mathcal{B}$-Open Sets",
  "authors": [
    "Layth M. Alabdulsada"
  ],
  "comment": "10 pages",
  "doi": "10.29020/nybg.ejpam.v12i2.3401",
  "categories": [
    "math.GN"
  ],
  "abstract": "The aim of this paper is to define and study $\\mathcal{B}$-open sets and related properties. A $\\mathcal{B}$-open set is, roughly speaking, a generalization of a $b$-open set, which is in turn a generalization of a pre-open set and a semi-open set. Using $\\mathcal{B}$-open sets, we introduce a number of concepts such as $\\mathcal{B}$-dense, $\\mathcal{B}$-Frechet, contra-$\\mathcal{B}$-closed graph and contra-$\\mathcal{B}$-continuity. Also, we define a bi-operator topological space $(X, \\tau, T_1, T_2)$ which involves two operators $T_1$ and $T_2$, which are used to define $\\mathcal{B}$-open sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-01T21:54:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C05",
      "54C08",
      "54C10"
    ],
    "keywords": [
      "generalization",
      "pre-open set",
      "semi-open set",
      "bi-operator topological space",
      "related properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}