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The example demonstrates that the chosen open cover $C$ of the finite space $X$ has a finite subcover $C_1$. This illustrates the core property used in the definition of compactness: every open cover admits a finite subcover.

Conditions: $X$ is the space under consideration.; $C$ is an open cover of $X$.; $C_1$ is a finite subcollection of $C$ covering $X$.

The example demonstrates that the chosen open cover $C$ of the finite space $X$ has a finite subcover $C_1$. This illustrates the core property used in the definition of compactness: every open cover admits a finite subcover.

Conditions: $X$ is the space under consideration.; $C$ is an open cover of $X$.; $C_1$ is a finite subcollection of $C$ covering $X$.