Geodesic
Cluster sets of a convergent sequence of continuous mappings
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 192-196.

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It is shown that the full cluster set of the pointwise convergent sequence of continuous mappings from complete metric space $X$ to a metric space $Y$ is degenerate on a residual set of points of $X$. 
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A. P. Devyatkov. Cluster sets of a convergent sequence of continuous mappings. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 192-196. http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a3/

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