Let $\mathrm{Map}(X,Y)$ denote the (unbased) cellular mapping space from $X$ to $Y$.

If $X$ and $Y$ are finite CW complexes, is $\mathrm{Map}(X,Y)$ a CW complex?

Can we know the cell structure of $\mathrm{Map}(X,Y)$?

For example, what is the cell structure of $\mathrm{Map}(S^n,S^k)$ for $n \geq k$?

Please recommend related papers and textbooks.