As we know,
For every $T_2$, first countable, compact space, its cardinality is not more than $2^\omega$. (See chapter 3 of Engelking's book.)
However, I want to know whether the result is same for the $T_2$, first countable, countably compact space, i.e., for every $T_2$, first countable, countably compact space, its cardinality is also not more than $2^\omega$?
Thanks for any help:)