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CHG would be "compact hausdorff generated" instead of "compactly-generated hausdorff" - this is a case where the letter order matters
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David White
David White
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I'm not quite certain what Peter May had in mind 40 years ago, but probably he had in mind the fact that pushouts are a lot better behaved in CGWH than in CHGCGH. Specifically, CHWHCGWH is closed under pushouts, one leg of which is the inclusion of a closed subspace. CHG CGH does not have such nice behavior, and pushouts like that are used all over The Geometry of Iterated Loop Spaces, specifically in the construction of a monad from an operad and in the use of geometric realizations of simplicial spaces.

I'm not quite certain what Peter May had in mind 40 years ago, but probably he had in mind the fact that pushouts are a lot better behaved in CGWH than in CHG. Specifically, CHWH is closed under pushouts, one leg of which is the inclusion of a closed subspace. CHG does not have such nice behavior, and pushouts like that are used all over The Geometry of Iterated Loop Spaces, specifically in the construction of a monad from an operad and in the use of geometric realizations of simplicial spaces.

I'm not quite certain what Peter May had in mind 40 years ago, but probably he had in mind the fact that pushouts are a lot better behaved in CGWH than in CGH. Specifically, CGWH is closed under pushouts, one leg of which is the inclusion of a closed subspace. CGH does not have such nice behavior, and pushouts like that are used all over The Geometry of Iterated Loop Spaces, specifically in the construction of a monad from an operad and in the use of geometric realizations of simplicial spaces.

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Peter May
Peter May
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I'm not quite certain what Peter May had in mind 40 years ago, but probably he had in mind the fact that pushouts are a lot better behaved in CGWH than in CHG. Specifically, CHWH is closed under pushouts, one leg of which is the inclusion of a closed subspace. CHG does not have such nice behavior, and pushouts like that are used all over The Geometry of Iterated Loop Spaces, specifically in the construction of a monad from an operad and in the use of geometric realizations of simplicial spaces.