In a topological KC-space, every compact space is closed.

In a US-space, each convergent sequence has a unique limit.

So, T2 ⇒ KC ⇒ US ⇒ T1, but the converse implications do not hold.

(a): Can you give me an easy example of a US-space that is not a KC-space?

(b): Is a product of KC-spaces also a KC-space?