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Given a finite semigroup S, define Φ(S) to be the intersection of all maximal subsemigroups of S, also known as the Frattini subsemigroup of S. The intersection number of S is the minimum number of maximal subsemigroups whose intersection is Φ(S). I will speak about a particular example of a semigroup with an interesting intersection number. In this example, the intersection number is equivalent to the minimum size of a subbasis of the discrete topology on a finite set, which is known.