{
  "abstract": "In this paper, we introduce and systematically investigate upper and lower semi-θ-continuous multifunctions and semi-θ-open multifunctions in the setting of bitopological spaces. The central concept underlying our approach is that of semi-ϕθ-open sets, defined via the θ-closure and θ-interior operators associated with the two topologies. We establish pointwise and global characterizations of upper semi-θ-continuity in terms of the semi-θ-interior and semi-θ-closure operators together with the upper and lower inverse mappings. Analogous characterizations are obtained for lower semi-θ-continuity, and we demonstrate through explicit examples that upper and lower semi-θ-continuity are independent notions, neither implying the other. We then introduce the dual concept of semi-θ-open multifunctions and derive several equivalent global characterizations, including the analogue of the classical result that a function is open precisely when the image of every open set is open. The interplay between upper semi-θ-continuity and semi-θ-openness is examined: the two notions are shown to be independent for multifunctions, while for bijective single-valued functions they coincide via the inverse mapping. Finally, we extend classical compactness, connectedness, and Hausdorffness to the semi-θ setting, establish their preservation and reflection properties under the relevant classes of multifunctions, and show via counterexamples that the multifunction analogues of certain single-valued results fail in the absence of disjoint-valuedness. The results unify and extend several known characterizations in the literature.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand",
    "Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus, Pattani 94000, Thailand",
    "Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Chawalit Boonpok",
      "orcid": "0000-0002-7933-6396"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Areeyuth Sama-Ae",
      "orcid": "0009-0009-2524-8129"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/034f931b3ps69.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193634",
  "fulltext_url": null,
  "id": "034f931b3ps69",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3634",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7221063279",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/034f931b3ps69.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193634",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3634"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Advanced Topology and Set Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Semi-θ-Continuous and Semi-θ-Open Multifunctions in Bitopological Spaces: Characterizations, Duality, and Topological Invariance",
  "title_text": "Semi-θ-Continuous and Semi-θ-Open Multifunctions in Bitopological Spaces: Characterizations, Duality, and Topological Invariance",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/034f931b3ps69",
  "venue": "Mathematics",
  "versions": []
}