{"doi":"10.15672/hujms.1121712","title":"On $T_1$-reflection of topological spaces","abstract":"<jats:p xml:lang=\"en\">This paper deals with some universal spaces. For every topological space $X$, the universal $T_1$ space is viewed as the bottom element of the lattice $\\mathcal{L}_X$. The class of morphisms in $\\mathrm{\\mathbf{Top}}$ orthogonal to all $T_1$ spaces is characterized. Also, we introduce some new separation axioms and characterize them. Moreover, we characterize topological spaces $X$ for which the universal $T_1$ space associated with $X$ is a spectral space. Finally, we give some characterizations of topological spaces such that their $T_1$-reflection are compact spaces.</jats:p>","journal":"Hacettepe Journal of Mathematics and Statistics","year":2023,"id":36220,"datarank":0.10397207708399181,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"self_citation_contribution":0.10397207708399181,"citation_network_contribution":0.0,"self_endowment_contribution":0.10397207708399181,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":1,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":183902,"name":"Abdelwaheb MHEMDİ","orcid":"0000-0002-9870-7148","position":1,"is_corresponding":false},{"id":183903,"name":"Tareq AL-SHAMİ","orcid":"0000-0002-8074-1102","position":2,"is_corresponding":false},{"id":183904,"name":"Hadjer OKBANİ","orcid":"0000-0003-1889-3583","position":3,"is_corresponding":false},{"id":183901,"name":"Sami LAZAAR","orcid":"0000-0002-3190-4251","position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"18998881","pmcid":null,"openalex_id":"https://openalex.org/W4306406217","authors":[],"funders":[],"total_grants":0,"fwci":0.1689,"citation_percentile":0.55014584,"influential_citations":0,"citation_trend":[{"year":2025,"count":1}],"oa_status":"gold","license":null,"oa_locations":[{"url":"https://doi.org/10.15672/hujms.1121712","host_type":"journal"},{"url":"https://dergipark.org.tr/en/download/article-file/2448811","host_type":"GOLD"},{"url":"https://doi.org/10.15672/hujms.1121712","host_type":"publisher"},{"url":"https://dergipark.org.tr/tr/pub/hujms/issue/76432/1121712","host_type":"repository"}],"fields_of_study":["Fuzzy and Soft Set Theory","Advanced Topology and Set Theory","Digital Image Processing Techniques","Mathematics"],"mesh_terms":[],"keywords":["Mathematics","Topological space","T1 space","Space (punctuation)","Separation axiom","Connected space","Topological algebra","Topological tensor product","Pure mathematics","Morphism","Separated sets","Zero-dimensional space","Topology (electrical circuits)","Topological vector space","Isolated point","Combinatorics","Functional analysis"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-10T14:54:31.743479Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}