On group operations on homogeneous spaces
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- by Yevhen Zelenyuk
- Proc. Amer. Math. Soc. 132 (2004), 1219-1222
- DOI: https://doi.org/10.1090/S0002-9939-03-07299-X
- Published electronically: November 7, 2003
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Abstract:
It is proved that every countably infinite homogeneous regular space admits a structure of any countably infinite group with continuous left shifts.References
- W. W. Comfort, Topological groups, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 1143–1263. MR 776643
- Neil Hindman and Dona Strauss, Algebra in the Stone-Čech compactification, De Gruyter Expositions in Mathematics, vol. 27, Walter de Gruyter & Co., Berlin, 1998. Theory and applications. MR 1642231, DOI 10.1515/9783110809220
- Talin Papazyan, Extremal topologies on a semigroup, Topology Appl. 39 (1991), no. 3, 229–243. MR 1110567, DOI 10.1016/0166-8641(91)90116-4
- I. V. Protasov, Filters and topologies on semigroups, Mat. Stud. 3 (1994), 15–28, 120 (Russian, with English and Russian summaries). MR 1692845
- E. G. Zelenjuk, Finite groups in $\beta \textbf {N}$ are trivial, Semigroup Forum 55 (1997), no. 1, 131–132. MR 1446665, DOI 10.1007/PL00005907
- Y. Zelenyuk, On topologies on groups with continuous shifts and inversion, (in Ukrainian) Visnyk Kyiv Univ., Ser. Fiz.-Mat. No. 2 (2000), 252–256.
Bibliographic Information
- Yevhen Zelenyuk
- Affiliation: Faculty of Cybernetics, Kyiv Taras Shevchenko University, vul. Glushkova 2, korp. 6, 03680, Kyiv, Ukraine
- Email: grishko@i.com.ua
- Received by editor(s): December 12, 2001
- Received by editor(s) in revised form: May 23, 2002
- Published electronically: November 7, 2003
- Communicated by: Alan Dow
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1219-1222
- MSC (2000): Primary 22A30, 54H11; Secondary 20A05, 54A05
- DOI: https://doi.org/10.1090/S0002-9939-03-07299-X
- MathSciNet review: 2045441