{
  "id": "2211.10631",
  "version": "v1",
  "published": "2022-11-19T09:38:31.000Z",
  "updated": "2022-11-19T09:38:31.000Z",
  "title": "Weakly meet $s_{Z}$-continuity and $δ_{Z}$-continuity",
  "authors": [
    "Huijun Hou",
    "Qingguo Li"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Based on the concept of weakly meet $s_{Z}$-continuouity put forward by Xu and Luo in \\cite{qzm}, we further prove that if the subset system $Z$ satisfies certain conditions, a poset is $s_{Z}$-continuous if and only if it is weakly meet $s_{Z}$-continuous and $s_{Z}$-quasicontinuous, which improves a related result given by Ruan and Xu in \\cite{sz}. Meanwhile, we provide a characterization for the poset to be weakly meet $s_{Z}$-continuous, that is, a poset with a lower hereditary $Z$-Scott topology is weakly meet $s_{Z}$-continuous if and only if it is locally weakly meet $s_{Z}$-continuous. In addition, we introduce a monad on the new category $\\mathbf{POSET_{\\delta}}$ and characterize its $Eilenberg$-$Moore$ algebras concretely.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-19T09:38:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A06",
      "18C15",
      "18C20"
    ],
    "keywords": [
      "continuity",
      "continuous",
      "subset system",
      "lower hereditary",
      "scott topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}