A Note on $Card(X)$ (Analysis in Theory and Applications, 2020)
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 $card({\cal F}(X→ Q))$.The main tool we used here is Zorn Lemma.
Keywords: Cardinality; separability of space; Zorn Lemma.