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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     author = {A. P. Devyatkov},
     title = {Cluster sets of a convergent sequence of continuous mappings},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     volume = {15},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a3/}
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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/