Discontinuity of bilaterally quasi-continuous transitional
functions

V. K. Maslyuchenko; V. V. Nesterenko

It is shown that the set of points of discontinuity of bilaterally quasi-continuous transitional function $f\colon \mathbb{R}\to \mathbb{R}$ has no isolated points. For any perfect nowhere dense subset $F$ of nondegenerate segment $J\subseteq \mathbb{R}$ bilaterally quasi-continuous transitional function $f\colon J\to \mathbb{R}$ such that $F$ is the set of points of discontinuity of $f$ is constructed.

1. Kretsu V.I., Maslyuchenko V.K. Stalling continuity, separate continuity and closed graph functions// Nauk. Visn. Chernivets’kogo Univ., Mat. – 2007. – V.349. – P. 50–54. (in Ukrainian)

2. Maslyuchenko V.K., Nesterenko V.V. Decomposition of continuity and transition maps// Mat. Visn. Nauk. Tov. Im. Shevchenka. – 2011. – V.8. – P. 132–150. (in Ukrainian)

3. Maslyuchenko V.K., Nesterenko V.V. Weak Darboux property and transitivity of linear mappings in topological vector spaces// Carp. Math. Publ. – 2013. – V.5, №1. – P. 79–88. (in Ukrainian)

4. Dobos J. Functions with a closed graph and bilateral quasicontinuity// Tatra Mt. Math. Publ. – 1993. – V.2. – P. 77–80.

5. Kechris A. Classical descriptive set theory. – Springer, 1995.

6. Aleksandrov P.S. Introduction to set theory and general topology. – M.: Nauka, 1977. (in Russian)

7. Banakh T.O., Maslyuchenko V.K., Mykhaylyuk V.V., Pshenychko M.I. Discontinuity points of almost continuous functions// Mat. Stud. – 2000. – V.14, №1. – P. 89–96. (in Ukrainian)

8. Gibson R.G., Natkaniec T. Darboux like functions// Real Anal. Exch. – 1997. – V.22, №2. – P. 492–533.

	Discontinuity of bilaterally quasi-continuous transitional functions(in Ukrainian)
Author	V. K. Maslyuchenko, V. V. Nesterenko math.analysis.chnu@gmail.com Yuriy Fedkovych Chernivtsi National University
Abstract	It is shown that the set of points of discontinuity of bilaterally quasi-continuous transitional function $f\colon \mathbb{R}\to \mathbb{R}$ has no isolated points. For any perfect nowhere dense subset $F$ of nondegenerate segment $J\subseteq \mathbb{R}$ bilaterally quasi-continuous transitional function $f\colon J\to \mathbb{R}$ such that $F$ is the set of points of discontinuity of $f$ is constructed.
Keywords	bilateral quasicontinuity; transitional function; set of points of discontinuity
DOI	doi:10.30970/ms.41.1.18-27
Reference	1. Kretsu V.I., Maslyuchenko V.K. Stalling continuity, separate continuity and closed graph functions// Nauk. Visn. Chernivets’kogo Univ., Mat. – 2007. – V.349. – P. 50–54. (in Ukrainian) 2. Maslyuchenko V.K., Nesterenko V.V. Decomposition of continuity and transition maps// Mat. Visn. Nauk. Tov. Im. Shevchenka. – 2011. – V.8. – P. 132–150. (in Ukrainian) 3. Maslyuchenko V.K., Nesterenko V.V. Weak Darboux property and transitivity of linear mappings in topological vector spaces// Carp. Math. Publ. – 2013. – V.5, №1. – P. 79–88. (in Ukrainian) 4. Dobos J. Functions with a closed graph and bilateral quasicontinuity// Tatra Mt. Math. Publ. – 1993. – V.2. – P. 77–80. 5. Kechris A. Classical descriptive set theory. – Springer, 1995. 6. Aleksandrov P.S. Introduction to set theory and general topology. – M.: Nauka, 1977. (in Russian) 7. Banakh T.O., Maslyuchenko V.K., Mykhaylyuk V.V., Pshenychko M.I. Discontinuity points of almost continuous functions// Mat. Stud. – 2000. – V.14, №1. – P. 89–96. (in Ukrainian) 8. Gibson R.G., Natkaniec T. Darboux like functions// Real Anal. Exch. – 1997. – V.22, №2. – P. 492–533.
Pages	18-27
Volume	41
Issue	1
Year	2014
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Discontinuity of bilaterally quasi-continuous transitional functions(in Ukrainian)