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I think this can be treated using a gluing theorem for homotopy equivalences which is discussed in my answer to this stackexchange questionstackexchange question. You have to represent the realisation of a simplicial space as a repeated adjunction space, but that is not too hard.

I think this can be treated using a gluing theorem for homotopy equivalences which is discussed in my answer to this stackexchange question. You have to represent the realisation of a simplicial space as a repeated adjunction space, but that is not too hard.

I think this can be treated using a gluing theorem for homotopy equivalences which is discussed in my answer to this stackexchange question. You have to represent the realisation of a simplicial space as a repeated adjunction space, but that is not too hard.

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Ronnie Brown
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I think this can be treated using a gluing theorem for homotopy equivalences which is discussed in my answer to this stackexchange question. You have to represent the realisation of a simplicial space as a repeated adjunction space, but that is not too hard.