A Note on $Card(X)$

Abstract

The main interests here are to study the relationship between $card(X)$ and $card({\cal P}(X))$ and the connection between the separability of a space $X$ and cardinality of some function space on it. We will convert the calculation of  $card({\cal P}(X))$ to the calculation of $card({\cal F}(X\rightarrow Q))$.The main tool we used here is Zorn Lemma.