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Explanation: Fourteen Sets Formed By Closure, Interior and Complement Operations
(related to Chapter: Basic Topological Concepts)
If $A$ is a set, we can create at most fourteen sets by successive application of the closure $A^$, interior $A^\circ$ and complement $A^C$ operations. These fourteen sets are:
 $A$
 $A^C$
 $A^\circ=A^{ C }$
 $A^$
 $A^{\circ C}$
 $A^{C}$
 $A^{\circ}$
 $A^{\circ}$
 $A^{\circ\circ}$
 $A^{\circ C\circ}$
 $A^{C\circ}$
 $A^{\circ }$
 $A^{\circ C\circ}$
 $A^{\circ \circ C}$
It is left to the reader as an exercise to build these 14 sets from this example subset of real numbers $\mathbb R$.
$$A:=\{\frac 1n\mid n=1,2,3\ldots\}\cup (2,3)\cup (3,4)\cup\left\{4 \frac 12\right\}\cup [6,7] \cup \{x\in \mathbb Q\mid 8\le x < 9\}$$
The example set is chosen in such a way that indeed all 14 sets are different. $(a,b)$ and $[a,b]$ denote open and closed real intervals.
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References
Bibliography
 Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984
 Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
 Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition