A topological space is called a sequential space if a set $A \subset X$ is closed if and only if together with any sequence it contains all its limits.
so, according to definition, is the following correct?
Sequential space has unique sequential limit iff each countably compact subset is clo...
These two questions ask about the same thing, the newer one asks for a proof, the older one asks about specific steps of a particular proof of this fact.
Brian M. Scott suggested closing the newer question as a duplicate.
The answer to the older question indeed answers the newer one.
It is not possible to cast a close vote on the older one, since the newer question has no answer (at this moment).
In general I would prefer the question asking about a specific proof to be closed as a duplicate. (If I would have to choose which of them has to be closed.)
But perhaps this is somewhat special case - probably not much can be said about the newer question that is not already contained in the older thread.
A sequential space has unique sequential limits iff each countably compact subset is closed.
Proof: If $ \{ x_n \} $ is a sequence converging to two distinc $x$ and $y$, then $ \{ x \} \cup \{ x_n : n \in \omega \} $ is a non compact se...
