Let G be a discrete groupoid. Consider the Stone–Čech compactification βG of G. We extend the operation on the set of composable elements G (2) of G to the operation * on a subset (βG)(2) of βG×βG such that the triple (βG, (βG)(2), *) is a compact right topological semigroupoid.
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References
M. Filali and I. Protasov, “Ultrafilters and topologies on groups,” Math. Stud. Monogr. Ser., VNTL, Lviv (2010).
M. Filali and T. Vedenjuoksu, “The Stone–Čech compactification of a topological group and the β-extension property,” Houston J. Math., 36, No. 2, 477–488 (2010).
L. Gillman and M. Jerison, Rings of Continuous Functions, van Nostrand, Princeton (1960).
N. Hindman and D. Strauss, Algebra in the Stone–Čech Compactification Theory and Applications, de Gruyter, Berlin (1998).
P. Muhly, Coordinates in Operator Algebra (Book in preparation).
A. L. T. Paterson, “Groupoids, inverse semigroups, and their operator algebras,” Progr. Math., Birkhäuser Boston Inc., Boston, MA, 170 (1999).
J. Renault, “A groupoid approach to C *-algebras,” Lect. Notes Math., 793 (1980).
R. Walker, The Stone–Čech Compactification, Springer, Berlin (1974).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 4, pp. 456–466, April, 2015.
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Behrouzi, F. The Stone–Čech Compactification of Groupoids. Ukr Math J 67, 515–527 (2015). https://doi.org/10.1007/s11253-015-1097-x
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DOI: https://doi.org/10.1007/s11253-015-1097-x