US not implies KC

This article gives the statement and possibly, proof, of a non-implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., US-space (?)) need not satisfy the second topological space property (i.e., KC-space (?))
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Statement

It is possible to have a US-space (i.e., a topological space in which every convergent sequence has at most one limit) that is not a KC-space.

Proof

Example of cofinite topology

Consider a countable set, say $X=\{1,2,3,\dots \}$, equipped with the cofinite topology. With this topology, the set is a US-space, because by definition, the only convergent sequence are those that are eventually constant, with the unique limit being the eventual constant value.

On the other hand, $X$ is not a KC-space, because, in fact, every subset of $X$ is compact, including the infinite proper subsets, which are not closed. To see why every subset of $X$ is compact, note that if $Y$ is a subset of $X$, any nonempty open subset of $Y$ is cofinite in $Y$. Hence, an open cover of $Y$ must have a finite subcover.