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Jun 1, 2020 at 18:04 comment added Dr. Dinesh J. Karia In fact, I am stuck with the following. There will be $(x_1, x_2), (x_3, x_4)$ such that $(a,b) = ( \pi(x_1), \pi(x_2))$ and $(b,c) = (\pi(x_3), \pi(x_4))$ and $(x_2,x_3) \in R$. In that case the composition of the above elements of $N$ is not possible. We must prove that for any entourage $N$ if $(x_1, x_2) \in N$ and $(x_2,x_3) \in R$, then $(x_1, x_3) \in N$
Dec 9, 2015 at 19:42 comment added M. A. I really appreciate your concern.
Dec 7, 2015 at 15:04 vote accept M. A.
Dec 7, 2015 at 14:17 vote accept M. A.
Dec 7, 2015 at 15:04
Dec 1, 2015 at 10:17 history answered Dominic van der Zypen CC BY-SA 3.0