{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T08:11:19Z","timestamp":1768637479186,"version":"3.49.0"},"reference-count":14,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,18]],"date-time":"2025-02-18T00:00:00Z","timestamp":1739836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The presented work enhances the study of topological characteristics in non-classical circumstances by examining Sg*-compact and Sg*-connected spaces in the context of generalized topological spaces. The notions of Sg*-compactness and Sg*-connectedness are explored better to understand their characteristics and behavior in these generalized topologies. Further, the study implements the same extended contexts to investigate the separation axioms, particularly T0, T1, and T2. The structural consequences of these axioms, which are essential for categorizing topological spaces according to the distinctness of points and sets, are examined. Since the premises of Sg*-compactness and Sg*-connectedness are not directly related to the separation axioms, exploring them independently enhances the analysis of generalized topology. This study serves as theoretical insights and establishes the foundation for future research in generalized topological spaces, contributing to their continued evolution.<\/jats:p>","DOI":"10.3390\/axioms14020141","type":"journal-article","created":{"date-parts":[[2025,2,18]],"date-time":"2025-02-18T12:16:37Z","timestamp":1739880997000},"page":"141","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some Categories of Compactness and Connectedness in Generalized Topological Spaces"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-7069-1753","authenticated-orcid":false,"given":"Muhammad","family":"Shahbaz","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-I-Azam University Islamabad, Islamabad 45320, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7833-2476","authenticated-orcid":false,"given":"Tayyab","family":"Kamran","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-I-Azam University Islamabad, Islamabad 45320, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5228-1073","authenticated-orcid":false,"given":"Umar","family":"Ishtiaq","sequence":"additional","affiliation":[{"name":"Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan"}]},{"given":"Mariam","family":"Imtiaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar Campus, Bahawalpur 63100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8042-1806","authenticated-orcid":false,"given":"Ioan-Lucian","family":"Popa","sequence":"additional","affiliation":[{"name":"Department of Computing, Mathematics and Electronics, \u201c1 Decembrie 1918\u201d University of Alba Iulia, 510009 Alba Iulia, Romania"},{"name":"Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania"}]},{"given":"Fethi Mohamed","family":"Maiz","sequence":"additional","affiliation":[{"name":"Physics Department, Faculty of Science, King Khalid University, Abha P.O. Box 9004, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF02843888","article-title":"Generalized closed sets in topology","volume":"19","author":"Levine","year":"1970","journal-title":"Rend. Del Circ. Mat. Di Palermo"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s10474-005-0005-5","article-title":"Generalized open sets in generalized topologies","volume":"106","year":"2005","journal-title":"Acta Math. Hung."},{"key":"ref_3","first-page":"2377","article-title":"On base for generalized topological spaces","volume":"6","author":"Khayyeri","year":"2011","journal-title":"Int. J. Contemp. Math. 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