Do the classes of pointed Hurewicz cofibrations, pointed Hurewicz fibrations and pointed homotopy equivalences give a model structure on pointed (compactly generated weak Hausdorff) topological spaces that is compatible with the smash product?


Maybe, this would work with another class of fibrations? (I am interested such a monoidal model structure with these precise classes of cofibrations and weak equivalences).


A reference is welcome!



A monoidal model structure on pointed spaces
Yes. According to [the nLab page for the Strom model structure](https://ncatlab.org/nlab/show/Str%C3%B8m+model+structure#monoidal_structure), this is proven in Section 6.4 of May's [Concise Course in Algebraic Topology](https://www.maths.ed.ac.uk/~v1ranick/papers/maybook.pdf). The point is that a closed inclusion is a cofibration if and only if it's an NDR pair, and you can use that to check that the pushout corner map is a (trivial) cofibration as required. Also, Donald Yau and I made use of this fact in Example 4.5 of [this](https://arxiv.org/pdf/1703.05359.pdf) paper.


