Geodesic
Normal functors on the category of paracompact $p$-spaces and their perfect mappings
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2012), pp. 61-63

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It is proved that for any paracompact $p$-space $X$ and any normal functor ${\mathscr F}$ of degree $\geq3$ in the category $\mathscr{P}$ the hereditary normality of the space $\mathscr{F}(X) \setminus X$ implies the metrizability of $X$. 
@article{VMUMM_2012_4_a12,
     author = {M. A. Dobrinina},
     title = {Normal functors on the category of paracompact $p$-spaces and their perfect mappings},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {61--63},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_4_a12/}
}
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M. A. Dobrinina. Normal functors on the category of paracompact $p$-spaces and their perfect mappings. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2012), pp. 61-63. http://geodesic.mathdoc.fr/item/VMUMM_2012_4_a12/