Geodesic
Nonincrease of Density and Weak Density under Weakly Normal Functors
Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 527-531

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In this paper, it is proved that if a covariant functor $\mathscr F\colon\mathrm{Comp}\to\mathrm{Comp}$ is weakly normal, then $d(\mathscr F^\beta(X))\le d(X)$ and $wd(\mathscr F^\beta(X))\le wd(X)$ for any infinite Tychonoff space $X$.
Keywords: normal functor, weakly normal functor, density, weak density, cellularity of a space, Tychonoff space, Stone–Čech compactification.
Mots-clés : Hausdorff space 
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     author = {R. B. Beshimov},
     title = {Nonincrease of {Density} and {Weak} {Density} under {Weakly} {Normal} {Functors}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {527--531},
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     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a4/}
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R. B. Beshimov. Nonincrease of Density and Weak Density under Weakly Normal Functors. Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 527-531. http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a4/