**Problem.** Assume that a compact space $X$ can be written as the union $X=K\cup D$ of a compact metrizable subspace $K$ and a discrete subspace $D$.
Does $D$ contain a non-trivial convergent sequence in $X$?

As shown by Ilya Bogdanov (http://mathoverflow.net/questions/254211/does-every-compact-countable-space-contain-a-non-trivial-convergent-sequence) the answer is affirmative if $K$ is at most countable.