nLab a Serre fibration between CW-complexes is a Hurewicz fibration

Statement

Theorem

Let $X$ and $Y$ be CW-complexes and $f:X\to Y$ a Serre fibration. Then $f$ is in fact a Hurewicz fibration (at least in a convenient category of spaces).

References

This was originally proven in

• Mark Steinberger and James West, Covering homotopy properties of maps between C.W. complexes or ANRs, Proc. Amer. Math. Soc. 92 (1984), 573-577, web page with fulltext PDF

An error was corrected in

• Robert Cauty, Sur les ouverts des CW-complexes et les fibrés de Serre, Colloquium Mathematicae (1992) Volume: 63, Issue: 1, page 1-7, web page with fulltext PDF