On limit sets of continuous functions with values ​​in locally linearly connected spaces

Maslyuchenko Oleksandr Volodymyrovych; Onypa Denys Pavlovich

On limit sets of continuous functions with values in locally linearly connected spaces

Maslyuchenko Oleksandr Volodymyrovych ^1,2 , Onypa Denys Pavlovich ²

¹ Institute of Mathematics, University of Silesia in Katowice, Katowice, 40-007, Poland

² Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: limit sets, continuous functions, linearly connected spaces

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Abstract

We prove that every subset $F$ of some locally arcwise connected metrizable compact $Y$ is the cluster set of a continuous function $f : (0;1] → Y$ at 0 if and only if it is nonempty closed and connected.

References

[1] Maslyuchenko O.V. The oscillation of quasicontinuous functions on pairwise attainable spaces // Houston Journal of Mathematics. 2009. - 35 , N1. - p. 113-130.

[2] Maslyuchenko O.V. Construction of $w$ -primaries: strongly achievable spaces // Mathematical Bulletin of the National Technical School. - 2009. - 6 . - p. 155-178.

[3] Maslyuchenko O.V., Onipa D.P. Limit oscillations of locally constant functions (in Russian) // Letters in Mathematics - 2013. - 1, N3-4. - p. 97-99.

[4] Maslyuchenko O.V., Onipa D.P. Construction of functions with given boundary sets // Sixteenth International Scientific Conference named after Academician Mykhailo Kravchuk. Kyiv, May 14-15, 2015 - National Technical University of Ukraine “KPI”. - 2015. - p. 137-139.

[5] Mazurkiewicz S. Sur les lignes de Jordan // Fund. Math. - 1920. - 1 . - p. 166-209.

[6] Bessaga C., Petczyński A. Selected topic in infinite-dimensional topology — Warszawa: PWN, 1975. - 353 p.

[7] Engelking R. General topology. - Moscow: Mir, 1986. - 752 p.

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Cite

ACS Style: Maslyuchenko, O.V.; Onypa, D.P. On limit sets of continuous functions with values in locally linearly connected spaces. Bukovinian Mathematical Journal. 2016, 3
AMA Style: Maslyuchenko OV, Onypa DP. On limit sets of continuous functions with values in locally linearly connected spaces. Bukovinian Mathematical Journal. 2016; 3(3-4).
Chicago/Turabian Style: Oleksandr Volodymyrovych Maslyuchenko, Denys Pavlovich Onypa. 2016. "On limit sets of continuous functions with values in locally linearly connected spaces". Bukovinian Mathematical Journal. 3 no. 3-4.

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