Minimal properties between T1 and T2

A space is a US-space if every convergent sequence has a unique limit; it is an SC-space if each convergent sequence together with its limit is closed and is a KC-space if every compact subset is closed. We study the existence of spaces which are minimal with respect to these properties. We develop a number of results regarding minimal SC-spaces, we show that the class of infinite minimal US-spaces is empty and we give a consistent example of a Tychonoff topology which contains no minimal KC-topology.