References

  1. Banakh T., Bardyla S. Characterizing chain-compact and chain-finite topological semilattices. Semigroup Forum 2019, 98 (2), 234–250. doi:10.1007/s00233-018-9921-x
  2. Banakh T., Bardyla S. Completeness and absolute H-closedness of topological semilattices. Topology Appl. 2019, 260, 189–202. doi:10.1016/j.topol.2019.04.001
  3. Banakh T., Bardyla S. On images of complete topologized subsemilattices in sequential semitopological semilattices. Semigroup Forum 2020, 100 (3), 662–670. doi:10.1007/s00233-019-10061-w
  4. Banakh T., Bardyla S. Complete topologized posets and semilattices. Topology Proc. 2021, 57, 177–196.
  5. Banakh T., Bardyla S. Characterizing categorically closed commutative semigroups. J. Algebra 2022, 591, 84–110. doi:10.1016/j.jalgebra.2021.09.030
  6. Banakh T., Bardyla S., Ravsky A. The closedness of complete subsemilattices in functionally Hausdorff semitopological semilattices. Topology Appl. 2019, 267, 106874. doi:10.1016/j.topol.2019.106874
  7. Bardyla S. Embedding of graph inverse semigroups into CLP-compact topological semigroups. Topology Appl. 2020, 272, 107058. doi:10.1016/j.topol.2020.107058
  8. Bardyla S. On topological McAlister semigroups. J. Pure Appl. Algebra 2023, 227 (4), 107274. doi:10.1016/j.jpaa.2022.107274
  9. Bardyla S., Gutik O. On a semitopological polycyclic monoid. Algebra Discrete Math. 2016, 21 (2), 163–183.
  10. Bertman M.O., West T.T. Conditionally compact bicyclic semitopological semigroups. Math. Proc. R. Ir. Acad. A 1976, 76 (21–23), 219–226.
  11. Carruth J.H., Hildebrant J.A., Koch R.J. The theory of topological semigroups, 1. In: Monographs and textbooks in pure and applied mathematics, 75. Marcel Dekker Inc., New York and Basel, 1983.
  12. Chuchman I.Ya., Gutik O.V. Topological monoids of almost monotone, injective co-finite partial selfmaps of positive integers. Carpathian Math. Publ. 2010, 2 (1), 119–132.
  13. Chuchman I., Gutik O. On monoids of injective partial selfmaps almost everywhere the identity. Demonstr. Math. 2011, 44 (4), 699–722. doi:10.1515/dema-2013-0340
  14. Clifford A.H., Preston G.B. The algebraic theory of semigroups, I. In: Mathematical surveys and monographs, 7. Amer. Math. Soc. Surveys , Providence, R.I., 1961.
  15. Clifford A.H., Preston G.B. The algebraic theory of semigroups, II. In: Mathematical surveys and monographs, 2. Amer. Math. Soc. Surveys , Providence, R.I., 1967.
  16. Eberhart C., Selden J. On the closure of the bicyclic semigroup. Trans. Amer. Math. Soc. 1969, 144, 115–126. doi:10.2307/1995273
  17. Engelking R. General topology. 2nd ed. Heldermann, Berlin, 1989.
  18. Gutik O. On locally compact semitopological \(0\)-bisimple inverse \(\omega\)-semigroups. Topol. Algebra Appl. 2018, 6, 77–101. doi:10.1515/taa-2018-0008
  19. Gutik O., Khylynskyi P. On the monoid of cofinite partial isometries of \(\mathbb{N}\) with a bounded finite noise. In: Walczak S. (Eds.) Proceedings of the Contemporary Mathematics in Kielce 2020. Sciendo, De Gruyter Poland Sp. z o.o. Warsaw, Poland, 2021, 127–144. doi:10.2478/9788366675360-010
  20. Gutik O., Lawson J., Repovš D. Semigroup closures of finite rank symmetric inverse semigroups. Semigroup Forum 2009, 78 (2), 326–336. doi:10.1007/s00233-008-9112-2
  21. Gutik O., Lysetska O. On the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}}\) which is generated by the family \(\mathscr{F}\) of atomic subsets of \(\omega\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2021, 92, 34–50.
  22. Gutik O., Mokrytskyi T. The monoid of order isomorphisms between principal filters of \(\mathbb{N}^n\). Eur. J. Math. 2020, 6 (1), 14–36. doi:10.1007/s40879-019-00328-5
  23. Gutik O., Mykhalenych M. On some generalization of the bicyclic monoid. Visnyk Lviv Univ. Ser. Mech.-Mat. 2020, 90, 5–19. (in Ukrainian). doi:10.30970/vmm.2020.90.005-019
  24. Gutik O.V., Pavlyk K.P. Topological semigroups of matrix units. Algebra Discrete Math. 2005, 3, 1–17.
  25. Gutik O., Pozdnyakova I. On monoids of monotone injective partial selfmaps of \(L_n\times_\mathrm{lex}\mathbb{Z}\) with cofinite domains and images. Algebra Discrete Math. 2014, 17 (2), 256–279.
  26. Gutik O.V., Reiter A.R. Symmetric inverse topological semigroups of finite rank \(\leqslant n\). J. Math. Sci. (N.Y.) 2010, 171 (4), 425–432. doi:10.1007/s10958-010-0147-z (reprint of Mat. Metody Fiz.-Mekh. Polya 2009, 52 (3), 7–14.)
  27. Gutik O., Repovš D. Topological monoids of monotone injective partial selfmaps of \(\mathbb{N}\) with cofinite domain and image. Studia Sci. Math. Hungar. 2011, 48 (3), 342–353. doi:10.1556/SScMath.48.2011.3.1176
  28. Gutik O., Repovš D. On monoids of injective partial selfmaps of integers with cofinite domains and images. Georgian Math. J. 2012, 19 (3), 511–532. doi:10.1515/gmj-2012-0022
  29. Gutik O., Savchuk A. On the semigroup \(\mathbf{ID}_{\infty}\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2017, 83, 5–19. (in Ukrainian)
  30. Gutik O., Savchuk A. On inverse submonoids of the monoid of almost monotone injective co-finite partial selfmaps of positive integers. Carpathian Math. Publ. 2019, 11 (2), 296–310. doi:10.15330/cmp.11.2.296-310
  31. Harzheim E. Ordered sets. In: Szép J. (Eds.) Advances in Mathematics, 7. Springer, New-York, 2005. doi:10.1007/b104891
  32. Lawson M.V. Inverse semigroups. The theory of partial symmetries. World Scientific, Singapore, 1998.
  33. Meakin J., Sapir M. Congruences on free monoids and submonoids of polycyclic monoids. J. Aust. Math. Soc. 1993, 54 (2), 236–253. doi:10.1017/S1446788700037149
  34. Mesyan Z., Mitchell J.D., Morayne M., Péresse Y.H. Topological graph inverse semigroups. Topology Appl. 2016, 208, 106–126. doi:10.1016/j.topol.2016.05.012
  35. Petrich M. Inverse semigroups. John Wiley \(\&\) Sons, New York, 1984.
  36. Ruppert W. Compact semitopological semigroups: an intrinsic theory. In: Morel J.-M., Teissier B. (Eds.) Lecture Notes in Mathematics, 1079. Springer, Berlin, 1984. doi:10.1007/BFb0073675
  37. Szendrei M.B. A generalization of McAlister's \(P\)-theorem for \(E\)-unitary regular semigroups. Acta Sci. Math. 1987, 51 (1–2), 229–249.
  38. Stepp J.W. A note on maximal locally compact semigroups. Proc. Amer. Math. Soc. 1969, 20, 251–253. doi:10.2307/2036002
  39. Stepp J.W. Algebraic maximal semilattices. Pacific J. Math. 1975, 58 (1), 243–248. doi:10.2140/pjm.1975.58.243
  40. Wagner V.V. Generalized groups. Dokl. Akad. Nauk SSSR 1952, 84, 1119–1122. (in Russian)