I'm writing an article on topology recently. I'm not good at English writing. It may be good for me to post this question somewhere else; however, I prefer to post here, as it is related to math.
My idea is this:
It is known that the cardinality of the compact metrizable space is always at most $2^\omega$. This is a necessary condition for a compact metrizable space. Therefore, it is necessary for one to discuss the cardinality of the space before trying to prove a space is compact metrizable.
Is this OK? Or is there a better way of expressing the idea? Thanks for your help.
(Sorry; I don't know how to tag it. I just want to attract one's attention.)