Past exam of the mathematics course of the University of Cambridge / 2013 / ib / Paper 2 / 4G / i

True. In a discrete topology, the singletons form an open cover. If $X$ is compact, a finite subcover exists, so $X$ is finite. Conversely, any open cover of a finite set has a finite subcover: choose one member containing each point. This converse does not require the discrete topology.