Geodesic
Weak normality of~$2^{X}$ and of~$X^{\tau}$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 1, pp. 135-140.

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It is proved that a weak normality of a space of closed subsets of a countably compact space $X$ implies that $X$ is compact. The example shows that the countable compactness of $X$ is essential. It is also proved that a weak normality of a sufficiently large power of $X$ implies that $X$ is compact. 
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     author = {A. P. Kombarov},
     title = {Weak normality of~$2^{X}$ and of~$X^{\tau}$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_1_a10/}
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A. P. Kombarov. Weak normality of~$2^{X}$ and of~$X^{\tau}$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 1, pp. 135-140. http://geodesic.mathdoc.fr/item/FPM_1998_4_1_a10/