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JOURNALS // Dal'nevostochnyi Matematicheskii Zhurnal // Archive

Dal'nevost. Mat. Zh., 2015 Volume 15, Number 2, Pages 192–196 (Mi dvmg308)

Cluster sets of a convergent sequence of continuous mappings

A. P. Devyatkov

Tyumen State University

Abstract: 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 $X$.

Key words: cluster set of sequence of functions, continuous convergence, meagre set.

UDC: 517.521

MSC: 54C05

Received: 21.07.2015



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