References

  1. Andersen O. Ein Bericht uber die Struktur abstrakter Halbgruppen. PhD Thesis, Hamburg, 1952.
  2. Anderson L.W., Hunter R.P. On the compactification of certain semigroups. Contrib. Extens. Theory Topol. Struct. Proc. Sympos. Berlin 1967. VEB Deutscher Verlag der Wissenschaften, Berlin, 1969, 21-27.
  3. Anderson L.W., Hunter R.P., Koch R.J. Some results on stability in semigroups. Trans. Amer. Math. Soc. 1965, 117, 521-529. dol:10.2307/1994222
  4. Arkhangel'skii A.V. Topological function spaces. Kluwer Publ., Dordrecht, 1992.
  5. Banakh T.O., Dimitrova S., Gutik O.V. The Rees-Suschkiewitsch Theorem for simple topological semigroups. Mat. Stud. 2009, 31 (2), 211-218.
  6. Banakh T., Dimitrova S., Gutik O. Embedding the bicyclic semigroup into countably compact topological semigroups. Topology Appl. 2010, 157 (18), 2803-2814. doi: 10.1016/j.topol.2010.08.020
  7. Bardyla S. Classifying locally compact semitopological polycyclic monoids. Math. Bull. Shevchenko Sci. Soc. 2016, 13, 21-28.
  8. Bardyla S. On a semitopological $\alpha$-bicyclic monoid. Visn. L'viv. Univ., Ser. Mekh.-Mat. 2016, 81, 9-22.
  9. Bardyla S. On locally compact shift-continuous topologies on the $\alpha$-bicyclic monoid. Topol. Algebra Appl. 2018, 6, 34-42. doi: 10.1515/taa-2018-0003
  10. Bardyla S. On locally compact semitopological graph inverse semigroups. Mat. Stud. 2018, 49 (1), 19-28. doi: 10.15330/ms.49.1.19-28
  11. Bardyla S. On locally compact topological graph inverse semigroups. Topology Appl. 2019, 267, 106873. doi: 10.1016/j.topol.2019.106873
  12. Bardyla S., Gutik O. On a semitopological polycyclic monoid. Algebra Discr. Math. 2016, 21 (2), 163-183.
  13. Bertman M.O., West T.T. Conditionally compact bicyclic semitopological semigroups. Proc. Roy. Irish Acad. 1976, A76 (21-23), 219-226.
  14. Carruth J.H., Hildebrant J.A., Koch R.J. The theory of topological semigroups. Vol. I, Marcel Dekker, Inc., New York and Basel, 1983; Vol. II, Marcel Dekker, Inc., New York and Basel, 1986.
  15. Chuchman I.Ya., Gutik O.V. Topological monoids of almost monotone injective co-finite partial selfmaps of the set of positive integers. Carpathian Math. Publ. 2010, 2 (1) 119-132.
  16. Clifford A.H., Preston G.B. The algebraic theory of semigroups. Vol. I., Amer. Math. Soc. Surveys 7, Providence, R.I., 1961; Vol. II., Amer. Math. Soc. Surveys 7, Providence, R.I., 1967.
  17. DeLeeuw K., Glicksberg I. Almost-periodic functions on semigroups. Acta Math. 1961, 105 (1-2), 99-140. doi: 10.1007/BF02559536
  18. Doroshenko V. Generators and relations for the semigroups of increasing functions on $\mathbb{N}$ and $\mathbb{Z}$. Algebra Discr. Math. 2005 (4), 1-15.
  19. Doroshenko V.V. On semigroups of order-preserving transformations of countable linearly ordered sets. Ukrainian Math. J. 2009, 61 (6), 859-872. doi: 10.1007/s11253-009-0256-3 (translation of Ukrainian Math. J. 2009, 61 (6), 723-732 (in Ukrainian))
  20. Engelking R. General topology. 2nd ed., Heldermann, Berlin, 1989.
  21. Fihel I.R., Gutik O.V. On the closure of the extended bicyclic semigroup. Carpathian Math. Publ. 2011, 3 (2), 131-157.
  22. Gutik O. On the dichotomy of a locally compact semitopological bicyclic monoid with adjoined zero. Visn. L'viv. Univ., Ser. Mekh.-Mat. 2015, 80, 33-41.
  23. Gutik O. Topological properties of Taimanov semigroups. Math. Bull. Shevchenko Sci. Soc. 2016, 13, 29-34.
  24. Gutik O. On locally compact semitopological $0$-bisimple inverse $\omega$-semigroups. Topol. Algebra Appl. 2018, 6, 77-101. doi: 10.1515/taa-2018-0008
  25. Gutik O., Maksymyk K. On semitopological interassociates of the bicyclic monoid. Visn. L'viv. Univ., Ser. Mekh.-Mat. 2016, 82, 98-108.
  26. Gutik O.V., Maksymyk K.M. On semitopological bicyclic extensions of linearly ordered groups. J. Math. Sci. 2019, 238 (1), 32-45. doi: 10.1007/s10958-019-04216-x
  27. Gutik O., Pozdnyakova I. On monoids of monotone injective partial selfmaps of $L_n\times_{\operatorname{lex}}\mathbb{Z}$ with co-finite domains and images. Algebra Discr. Math. 2014, 17 (2), 256-279.
  28. Gutik O., Repovš D. On countably compact $0$-simple topological inverse semigroups. Semigroup Forum 2007, 75 (2), 464-469. doi: 10.1007/s00233-007-0706-x
  29. Gutik O., Repovš D. Topological monoids of monotone, injective partial selfmaps of $\mathbb{N}$ having cofinite domain and image. Studia Sci. Math. Hungar. 2011, 48 (3), 342-353. doi: 10.1556/SScMath.48.2011.3.1176
  30. 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
  31. Gutik O., Savchuk A. On the semigroup $\mathbf{ID}_{\infty}$. Visn. Lviv. Univ., Ser. Mekh.-Mat. 2017, 83, 5-19. (in Ukrainian)
  32. Gutik O., Savchuk A. The semigroup of partial co-finite isometries of positive integers. Bukovyn. Mat. Zh. 2018, 6 (1-2), 42-51. doi: 10.31861/bmj2018.01.042 (in Ukrainian)
  33. Hildebrant J.A., Koch R.J. {\it Swelling actions of $\Gamma$-compact semigroups. Semigroup Forum 1986, 33 (1), 65-85. doi: 10.1007/BF02573183
  34. Hogan J.W. The $\alpha$-bicyclic semigroup as a topological semigroup. Semigroup forum 1984, 28 (1), 265-271. doi: 10.1007/BF02572488
  35. Lawson M. V. Inverse semigroups. The theory of partial symmetries. World Scientific, Singapore, 1998.
  36. Mesyan Z., Mitchell J.D., Morayne M., P\'{e}resse Y.H. Topological graph inverse semigroups. Topology Appl. 2016, 208, 106-126. doi: 10.1016/j.topol.2016.05.012
  37. Munn W.D. The algebra of a combinatorial inverse semigroup. J. Lond. Math. Soc., II. Ser. 1983, 27 (1), 35-38. doi: 10.1112/jlms/s2-27.1.35
  38. Petrich M. Inverse semigroups. John Wiley $\&$ Sons, New York, 1984.
  39. Ruppert W. Compact semitopological semigroups: an intrinsic theory. Lect. Notes Math., 1079, Springer, Berlin, 1984. doi: 10.1007/BFb0073675
  40. Selden A.A. A nonlocally compact nondiscrete topology for the $\alpha$-bicyclic semigroup. Semigroup Forum 1985, 31 (1), 372-374. doi: 10.1007/BF02572664
  41. Taimanov A.D. An example of a semigroup which admits only the discrete topology. Algebra and Logic 1973, 12 (1), 64-65. doi: 10.1007/BF02218642 (translation of Algebra i Logika 1973, 12 (1), 114-116 (in Russian))
  42. Taimanov A.D. On the topologization of commutative semigroups. Math. Notes 1975, 17 (5), 443-444. doi: 10.1007/BF01155800 (translation of Mat. Zametki 1975, 17 (5), 745-748 (in Russian))
  43. Wagner V.V. Generalized groups. Dokl. Akad. Nauk SSSR 1952, 84, 1119-1122 (in Russian).