Right-topological semigroup operations on inclusion hyperspaces

V.Gavrylkiv

We show that for any discrete semigroup $X$ the semigroup operation can be extended to a right-topological semigroup operation on the space $G(X)$ of inclusion hyperspaces on $X$. We detect some important subsemigroups of $G(X)$, study the minimal ideal, the (topological) center, left and right cancelable elements of $G(X).$

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2. T.Banakh, V.Gavrylkiv, O.Nykyforchyn, Algebra in the superextensions of groups// Мат. Студії (submitted).

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4. V.Gavrylkiv. The spaces of inclusion hyperspaces over non-compact spaces, Matem. Studii 28(2007), 92--110.

5. А.В.~Иванов. Теорема о почти неподвижной точке для пространства полных к-сцепленных систем, Вопросы геометрии и топологии. Петрозаводск, 1986. -- C. 31--40.

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8. N.Hindman, D.Strauss, Algebra in the Stone- Cech compactification, de Gruyter, Berlin, New York, 1998.

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11. I.Protasov. Combinatorics of Numbers, VNTL, Lviv, 1997.

12. I.Protasov, The topological center of semigroups of free ultrafilters, Mat. Zametki, 63 (1998), 437--441; transl. in: Math. Notes 63 (2003), 437--441.

13. A.Teleiko, M.Zarichnyi. Categorical Topology of Compact Hausdofff Spaces, VNTL, Lviv, 1999.

	Right-topological semigroup operations on inclusion hyperspaces
Author	V.Gavrylkiv vgavrylkiv@yahoo.com V. Stefanyk Pre-Carpathian National University
Abstract	We show that for any discrete semigroup $X$ the semigroup operation can be extended to a right-topological semigroup operation on the space $G(X)$ of inclusion hyperspaces on $X$. We detect some important subsemigroups of $G(X)$, study the minimal ideal, the (topological) center, left and right cancelable elements of $G(X).$
Keywords	discrete semigropup, right-topological semigroup operation, inclusion hyperspace
DOI	doi:10.30970/ms.29.1.18-34
Reference	1. T.Banakh, L.Zdomskyy. Coherence of Semifilters, (available at: \\ http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/booksite.html) 2. T.Banakh, V.Gavrylkiv, O.Nykyforchyn, Algebra in the superextensions of groups// Мат. Студії (submitted). 3. O.~Chein, H.O.Pflugfelder, J.D.Smith (eds.), Quasigroups and loops: theory and applications, Sigma Series in Pure Math. 8, Heldermann Verlag, Berlin, 1990. 4. V.Gavrylkiv. The spaces of inclusion hyperspaces over non-compact spaces, Matem. Studii 28(2007), 92--110. 5. А.В.~Иванов. Теорема о почти неподвижной точке для пространства полных к-сцепленных систем, Вопросы геометрии и топологии. Петрозаводск, 1986. -- C. 31--40. 6. N.Hindman, Finite sums from sequences within cells of partition of $\mathbb N$, J.~Combin. Theory Ser. A 17 (1974), 1--11. 7. N.Hindman, Ultrafilters and combinatorial number theory, Lecture Notes in Math. 751 (1979), 49--184. 8. N.Hindman, D.Strauss, Algebra in the Stone- Cech compactification, de Gruyter, Berlin, New York, 1998. 9. E.Moiseev. Superextentions of normal spaces, Vestn. Moscow Univ., (1990), № 2, 80-83 (Russian). 10. H.~Pflugfelder, Quasigroups and loops: introduction, Sigma Series in Pure Math. 7, Heldermann Verlag, Berlin, 1990. 11. I.Protasov. Combinatorics of Numbers, VNTL, Lviv, 1997. 12. I.Protasov, The topological center of semigroups of free ultrafilters, Mat. Zametki, 63 (1998), 437--441; transl. in: Math. Notes 63 (2003), 437--441. 13. A.Teleiko, M.Zarichnyi. Categorical Topology of Compact Hausdofff Spaces, VNTL, Lviv, 1999.
Pages	18-34
Volume	29
Issue	1
Year	2008
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html