{
  "id": "2407.17752",
  "version": "v1",
  "published": "2024-07-25T04:07:26.000Z",
  "updated": "2024-07-25T04:07:26.000Z",
  "title": "Composition of locally solid convergences",
  "authors": [
    "Eugene Bilokopytov"
  ],
  "comment": "17 pages, preliminary version",
  "categories": [
    "math.FA"
  ],
  "abstract": "We carry on a more detailed investigation of the composition of locally solid convergences as introduced in \\cite{ectv}, as well as the corresponding notion of idempotency considered in \\cite{erz}. In particular, we study the interactions between these two concepts and various operations with convergences. Some results from \\cite{kt} about unbounded modification of locally solid topologies are generalized to the level of locally solid idempotent convergences. A simple application of the composition allows us to answer a question from \\cite{ectv} about minimal Hausdorff locally solid convergences. We also show that the weakest Hausdorff locally solid convergence exists on an Archimedean vector lattice if and only if it is atomic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-25T04:07:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A19",
      "46A40",
      "46B42",
      "46E25",
      "54A20"
    ],
    "keywords": [
      "composition",
      "weakest hausdorff locally solid convergence",
      "minimal hausdorff locally solid convergences",
      "locally solid idempotent convergences",
      "archimedean vector lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}