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Daniel Moskovich
Daniel Moskovich
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WeLet $\mathrm{Map}(X,Y)$ denote Map$(X,Y)$the (unbased) cellular mapping spacesspace from $X$ to $Y$.

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

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

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

Please recommend related papers and textbooks.

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.

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.

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Jino
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.