Far Eastern Mathematical Journal

To content of the issue


Cluster sets of a convergent sequence of continuous mappings


Devyatkov A.P.

2015, issue 2, . 192-196


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.

Keywords:
cluster set of sequence of functions, continuous convergence, meagre set

Download the article (PDF-file)

References

[1] V.I. Kruglikov, "Predel'nye mnozhestva posledovatel'nosti funkcij", Dokl. RAN, 357:1 (1997), 16-18.
[2] K. Nosiro, Predel'nye mnozhestva, IL, M., 1963.
[3] Je. Kollingvud, A. Lovater, Teorija predel'nyh mnozhestv, Mir, M., 1971.
[4] A. Lovater, "Granichnoe povedenie analiticheskih funkcij", Itogi nauki i tehniki. Matematicheskij analiz. T. 10, VINITI, 1973, 99-259.
[5] S. Stoilow, "Asupra convergentei continue", Studii ?i Cercetari Mat., 7 (1956), 247-250.

To content of the issue