{
  "id": "2112.07298",
  "version": "v2",
  "published": "2021-12-14T11:10:49.000Z",
  "updated": "2023-01-23T15:07:59.000Z",
  "title": "Embedding Theorems for function spaces",
  "authors": [
    "Mikhail Al'perin",
    "Sergei Nokhrin",
    "Alexander V. Osipov"
  ],
  "comment": "29 pages",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology of pointwise convergence into the Tychonoff product of topological spaces, but applied to the function space $C(X,Y)$ of all continuous functions from a topological space $X$ into a uniform space $Y$ with the topology of uniform convergence on a family of subsets of $X$ and with the (weak) set-open topology. We also investigated the following question: how the topological embedding of the space $C(X,Y)$ is related to algebraic structures (such as topological groups, topological rings and topological vector spaces) on $C(X,Y)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-01-23T15:07:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "function space",
      "embedding theorems",
      "topological space",
      "tychonoffs theorem",
      "topological vector spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}