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Jino
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All mapping space between CW complexes is a CW complex?

We denote Map$(X,Y)$ (unbased) mapping spaces from $X$ to $Y$.

If $X$ and $Y$ are finite CW complexes, $map(X,Y)$ is a CW complex?

Can we know the cell structure of Map$(X,Y)$?

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

Please recommend related papers and textbooks.

Jino
  • 699
  • 5
  • 14