Consider the set X={a,b,c,d} with the discrete topology, construct a sub-basis of the space that does not have any unitary set. That is, a set that can generate the topology described by the union and intersection of its elements.   Please be as clear as possible showing the steps and giving definitions if necessary. Thak you a lot

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Consider the set X={a,b,c,d} with the discrete topology, construct a sub-basis of the space that does not have any unitary set. That is, a set that can generate the topology described by the union and intersection of its elements.
 
Please be as clear as possible showing the steps and giving definitions if necessary. Thak you a lot
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