In his 1967 paper A convenient category of topological spaces, Norman Steenrod introduced the category CGH of compactly generated Hausdorff spaces as a good replacement of the catgory Top topological spaces, in order to do homotopy theory.

The most important defference between CGH and Top is that in CGH there is a functorial homeomorphism $$\mathrm{map}(X,\mathrm{map}(Y,Z))\cong \mathrm{map}(X\times Y,Z),$$ a fact that is only true in Top under the extra assumption that $Y$ is locally compact.

But in more recent papers, I see that people use CGWH spaces instead of CGH spaces... Why?

Could someone explain to me what goes wrong in CGH spaces (please illustrate with an example),
and explain how the "w" fixes everything?

Also (following Jeff's comment), to whom should the "w" be attributed?

One more wish: can someone give me an example of a CGWH space that isn't CGH?

In his 1967 paper A convenient category of topological spaces, Norman Steenrod introduced the category CGH of compactly generated Hausdorff spaces as a good replacement of the category Top topological spaces, in order to do homotopy theory.

The most important difference between CGH and Top is that in CGH there is a functorial homeomorphism $$\mathrm{map}(X,\mathrm{map}(Y,Z))\cong \mathrm{map}(X\times Y,Z),$$ a fact that is only true in Top under the extra assumption that $Y$ is locally compact.

But in more recent papers, I see that people use CGWH spaces instead of CGH spaces... Why?

Could someone explain to me what goes wrong in CGH spaces (please illustrate with an example),
and explain how the "w" fixes everything?

Also (following Jeff's comment), to whom should the "w" be attributed?

One more wish: can someone give me an example of a CGWH space that isn't CGH?

In his 1967 paper A convenient category of topological spaces, Norman Steenrod introduced the category CGH of compactly generated Hausdorff spaces as a good replacement of the catgory Top topological spaces, in order to do homotopy theory.

The most important defference between CGH and Top is that in CGH there is a functorial homeomorphism $$\mathrm{map}(X,\mathrm{map}(Y,Z))\cong \mathrm{map}(X\times Y,Z),$$ a fact that is only true in Top under the extra assumption that $Y$ is locally compact.

But in more recent papers, I see that people use CGWH spaces instead of CGH spaces... Why?

Could someone explain to me what goes wrong in CGH spaces (please illustrate with an example),
and explain how the "w" fixes everything?

Also (following Jeff's comment), to whom should the "w" be attributed?

In his 1967 paper A convenient category of topological spaces, Norman Steenrod introduced the category CGH of compactly generated Hausdorff spaces as a good replacement of the catgory Top topological spaces, in order to do homotopy theory.

The most important defference between CGH and Top is that in CGH there is a functorial homeomorphism $$\mathrm{map}(X,\mathrm{map}(Y,Z))\cong \mathrm{map}(X\times Y,Z),$$ a fact that is only true in Top under the extra assumption that $Y$ is locally compact.

But in more recent papers, I see that people use CGWH spaces instead of CGH spaces... Why?

Could someone explain to me what goes wrong in CGH spaces (please illustrate with an example),
and explain how the "w" fixes everything?

Also (following Jeff's comment), to whom should the "w" be attributed?

One more wish: can someone give me an example of a CGWH space that isn't CGH?

In his 1967 paper A convenient category of topological spaces, Norman Steenrod introduced the category CGH of compactly generated Haudorff spaces as a good replacement of the catgory Top topological spaces, in order to do homotopy theory.

The most important defference between CGH and Top is that in CGH there is a functorial homeomrphism $$\mathrm{map}(X,\mathrm{map}(Y,Z))\cong \mathrm{map}(X\times Y,Z),$$ a fact that is only true in Top under the extra assumption that $Y$ is locally compact.

But in more recent papers, I see that people use CGWH spaces instead of CGH spaces... Why?

Could someone explain to me what goes wrong in CGH spaces (and illustrate it with an example),
and explain how the "w" fixes everything?

In his 1967 paper A convenient category of topological spaces, Norman Steenrod introduced the category CGH of compactly generated Hausdorff spaces as a good replacement of the catgory Top topological spaces, in order to do homotopy theory.

The most important defference between CGH and Top is that in CGH there is a functorial homeomorphism $$\mathrm{map}(X,\mathrm{map}(Y,Z))\cong \mathrm{map}(X\times Y,Z),$$ a fact that is only true in Top under the extra assumption that $Y$ is locally compact.

But in more recent papers, I see that people use CGWH spaces instead of CGH spaces... Why?

Could someone explain to me what goes wrong in CGH spaces (please illustrate with an example),
and explain how the "w" fixes everything?

Also (following Jeff's comment), to whom should the "w" be attributed?