{
  "abstract": "We study exponentiable objects and function spaces in the category of stratified Lowen fuzzy topological spaces over \\(\\I=[0,1]\\). Using the Lowen fuzzy Sierpiński object \\(\\Sier\\), which identifies \\(τ_X\\) with \\(C(X,\\Sier)\\), we explicitly determine the largest splitting topology on this mapping set. Its open weights \\(Φ:τ_X\\to\\I\\) are precisely those satisfying Scott continuity and a finite-tier compatibility condition induced by finite powers of \\(\\Sier\\). This yields an intrinsic characterization: \\(X\\) is exponentiable if and only if every \\(μ\\inτ_X\\) satisfies \\[ μ=\\bigvee_{λ\\triangleleftΦ} (\\const{Φ(μ)}\\wedgeλ), \\qquad λ\\triangleleftΦ \\Longleftrightarrow \\const{Φ(ν)}\\wedgeλ\\leqν \\quad(ν\\inτ_X). \\] When this condition holds, \\(Y^X\\) has underlying set \\(C(X,Y)\\), with topology generated by \\([Φ,v](f)=Φ(v\\circ f)\\). We also obtain a dual closed-set formulation and three applications. Exponentiability implies that \\(τ_X\\) is a continuous lattice, although the converse fails. Moreover, a classical space \\(X\\) is exponentiable exactly when its induced fuzzy space \\(ωX\\) is exponentiable in the entire stratified Lowen category. Finally, Lowen compact, strongly fuzzy compact, and \\(N\\)-compact Hausdorff spaces are exponentiable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23281",
  "author_total": 1,
  "authors": [
    {
      "name": "Yongming Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bp1h9ym4z42vk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23281",
  "fulltext_url": null,
  "id": "bp1h9ym4z42vk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23281",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7214005535",
  "pdf_url": "https://arxiv.org/pdf/2609.23281",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bp1h9ym4z42vk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23281",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23281"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Exponentiable Objects and Function spaces in Lowen Fuzzy Topological Spaces",
  "title_text": "Exponentiable Objects and Function spaces in Lowen Fuzzy Topological Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/bp1h9ym4z42vk",
  "venue": "arXiv",
  "versions": []
}