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Definition: Discrete and Indiscrete Topology
It is easily verified from the axioms of a topology that every set $X$ together has two particular topologies:
 its power set $\mathcal P(X)$ (containing all possible subsets of $X$), called the discrete topology of $X,$ and
 the set $\{X,\emptyset\},$ (containing the greatest and the smallest subset of $X$), called the indiscrete topology of $X.$
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Definitions: 1
Examples: 2 3
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References
Bibliography
 Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970