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Topology on Equality Algebras

dc.contributor.authorAaly Kologani, Mona
dc.contributor.authorNiazian, Sogol
dc.contributor.authorBorzooei, Rajab Ali
dc.date.accessioned2026-07-02T09:18:48Z
dc.date.available2026-07-02T09:18:48Z
dc.date.issued2026-06-10
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/58693
dc.description.abstractIn this paper, by special upsets on equality algebras, we construct a topology on bounded equality algebras and investigate some of their topological properties, such as Hausdorff, T0-space, T1-space and disconnected. In addition, we express the relation between closed and compact sets in this topology. Moreover, by considering the binary operation ↠ and constructing a topology on the bounded equality algebra E, we introduce the notion of semi-topological algebra and prove that any involutive equality algebra is a right semi-topological algebra and by some conditions it can be a semi-⋏-topological algebra. Also, we show that it is not necessarily a left semi-topological algebra. Finally, we investigate converse image, product and quotient topology on equality algebra and show that under what condition we can make finer topology.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;2en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectequality algebraen
dc.subjectupseten
dc.subjecttopologyen
dc.subjectproduct topologyen
dc.subjectquotient topologyen
dc.titleTopology on Equality Algebrasen
dc.typeOther
dc.page.number219-245
dc.contributor.authorAffiliationAaly Kologani, Mona - Hatef Higher Education Institute, Zahedan, Iranen
dc.contributor.authorAffiliationNiazian, Sogol - TeMS. C, Islamic Azad University, Faculty of Medicine, Tehran, Iranen
dc.contributor.authorAffiliationBorzooei, Rajab Ali - Shahid Beheshti University, Faculty of Mathematical Sciences, Department of Mathematics, Tehran, Iranen
dc.identifier.eissn2449-836X
dc.referencesR. Borzooei, N. Kouhastani, M. A. Kologani, On (semi)topological hoop algebras, Quasigroups and Related Systems, vol. 27 (2019), pp. 161–174.en
dc.referencesR. Borzooei, G. R. Rezaei, N. Kouhastani, On (semi)topological BL-algebras, Iranian Journal of Mathematical Sciences and Informatics, vol. 6(1) (2011), pp. 59–77.en
dc.referencesR. Borzooei, G. R. Rezaei, N. Kouhastani, Metrizability on (semi)topological BL-algebras, Soft Computing, vol. 16(10) (2012), pp. 1681–1690, DOI: https://doi.org/10.1007/s00500-012-0852-2.en
dc.referencesR. Borzooei, G. R. Rezaei, N. Kouhastani, Separation axioms in (semi)topological quotient BL-algebras, Soft Computing, vol. 16(7) (2012), pp. 1219–1227, DOI: https://doi.org/10.1007/s00500-012-0808-6.en
dc.referencesR. A. Borzooei, M. Zarean, O. Zahiri, Involutive equality algebras, Soft Computing, vol. 22 (2018), pp. 7505–7517, DOI: https://doi.org/10.1007/s00500-018-3032-1.en
dc.referencesR. A. Borzooei, F. Zebardast, M. A. Kologani, Some types of filters in equality algebras, Categories and General Algebraic Structures with Applications, vol. 7(1) (2017), pp. 33–55.en
dc.referencesM. Dyba, V. Novák, EQ-logics with delta connective, Iranian Journal of Fuzzy Systems, vol. 12(2) (2015), pp. 41–61.en
dc.referencesS. Jenei, Equality algebras, Studia Logica, vol. 100(6) (2012), pp. 1201–1209, DOI: https://doi.org/10.1007/s11225-012-9398-9.en
dc.referencesM. A. Kologani, On (semi)topology L -algebras, Categories and General Algebraic Structures with Applications, vol. 18(1) (2023), pp. 81–103, DOI: https://doi.org/10.52547/cgasa.18.1.81.en
dc.referencesM. A. Kologani, Relations between L-algebras and other logical algebras, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 4(1) (2023), pp. 27–46.en
dc.referencesM. A. Kologani, R. Borzooei, G. R. Rezaei, Y. B. Jun, Commutative equality algebras and & -equality algebras, Annals of the University of Craiova, Mathematics and Computer Science Series, vol. 47(2) (2020), pp. 331–345.en
dc.referencesM. A. Kologani, M. M. Takallo, R. Borzooei, Y. B. Jun, Implicative equality algebras and annihilators in equality algebras, Journal of Discrete Mathematical Sciences and Cryptography, (2021), DOI: https://doi.org/10.1080/09720529.2021.1876293.en
dc.referencesM. A. Kologani, M. M. Takallo, R. Borzooei, Y. B. Jun, Right and left mappings in equality algebras, Kragujevac Journal of Mathematics, vol. 45(5) (2022), pp. 815–832, DOI: https://doi.org/10.46793/KgJMat2205.815K.en
dc.referencesJ. R. Munkres, Topology: A First Course, Prentice-Hall (1974).en
dc.referencesS. Niazian, Prime filters and Zariski topology on equality algebras, International Journal of Industrial Mathematics, vol. 15(2) (2023), pp. 137–150.en
dc.referencesS. Niazian, M. A. Kologani, R. A. Borzooei, On co-annihilators in equality algebras, Miskolc Mathematical Notes, vol. 24(2) (2023), pp. 933–951, DOI: https://doi.org/10.18514/MMN.2023.3816.en
dc.referencesV. Novák, B. D. Baets, EQ-algebras, Fuzzy Sets and Systems, vol. 160(20) (2009), pp. 2956–2978, DOI: https://doi.org/10.1016/j.fss.2009.04.010.en
dc.referencesA. Paad, Ideals in bounded equality algebras, Filomat, vol. 33(7) (2019), pp. 2113–2123, DOI: https://doi.org/10.2298/FIL1907113P.en
dc.referencesG. R. Rezaei, M. A. Kologani, R. A. Borzooei, M. M. Takallo, Derivations of equality algebras, Soft Computing, vol. 26 (2022), pp. 5057–5067, DOI: https://doi.org/10.1007/s00500-022-06972-6.en
dc.referencesM. M. Takallo, M. A. Kologani, MBJ-neutrosophic filters of equality algebras, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 1(2) (2020), pp. 57–75.en
dc.referencesX. L. Xin, M. Khan, Y. B. Jun, Generalized states on EQ-algebras, Iranian Journal of Fuzzy Systems, vol. 16(1) (2019), pp. 159–172.en
dc.referencesO. Zahiri, On a new sum of equality algebras, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 5(1) (2024), pp. 87–94.en
dc.referencesO. Zahiri, R. A. Borzooei, Topology on BL-algebras, Fuzzy Sets and Systems, vol. 289 (2016), pp. 137–150, DOI: https://doi.org/10.1016/j.fss.2015.10.023.en
dc.referencesF. Zebardast, R. A. Borzooei, M. A. Kologani, Results on equality algebras,Information Sciences, vol. 381 (2017), pp. 270–282, DOI: https://doi.org/10.1016/j.ins.2016.11.027.en
dc.contributor.authorEmailAaly Kologani, Mona - mona4011@gmail.com
dc.contributor.authorEmailNiazian, Sogol - s.niazian@iau.ac.ir
dc.contributor.authorEmailBorzooei, Rajab Ali - borzooei@sbu.ac.ir
dc.identifier.doi10.18778/0138-0680.2026.07
dc.relation.volume55


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