Alexandroff spaces are the topological spaces in which the intersection of arbitrary many open sets is open. Let T be an indecomposable tournament. In this paper, first, we associate a trivial topology to T. Then we define another topology on T, called the graphic topology of T, and we show that it is an Alexandroff topology. Our motivation is to investigate some properties of this topology.
Funding statement: We would also like to thank Campus France for support through PHC Maghreb program.
We sincerely thank the anonymous reviewer for constructive criticisms and valuable comments that much improved the manuscript.
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