The discontinuity point set of A-continuous functions (in Ukrainian)

Author O. V. Maslyuchenko
ovmasl@gmail.com
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Abstract We characterize the set of discontinuity points of A-continuous quasi-continuous functions of the first class defined on hereditarily normal weakly pairwise attainable spaces. Besides, we obtain several sufficient properties of a subset of a normed space which guarantee an existence of a linearly continuous function with the given discontinuity point set.
Keywords A-continuous function; discontinuity point set; quasi-continuous function; linearly continuous function; A-nowhere dense set; $\sigma$-A-nowhere dense set
Reference 1. V.K. Maslyuchenko, V.V. Mykhalyuk, A charecterization of the discontinuty point set of separately continuous functions of several variable defined on the product of metrizable spaces, Ukr. mat. zhurnal, 52 (2000), ¹6, 740–747. (in Ukrainian)

2. O.V. Maslyuchenko, Construction of $\omega$-primitives: the strongly attaineble spaces, Mat. visnyk NTSh, 6 (2009), 155–178. (in Ukrainian)

3. O.V. Maslyuchenko, The oscillation of quasi-continuous functions on pairwise attainable spaces, Houston Journal of Mathematics, 35 (2009), ¹1, 113–130.

4. O.V. Maslyuchenko, The discontinuity point sets of quasi-continuous functions, Bul. Austral. Math. Soc., 75 (2007), ¹3, 373–379.

5. R. Engelking, General topology. – Warszawa: PWN, 1977. – 626 p.

Pages 89-97
Volume 37
Issue 1
Year 2012
Journal Matematychni Studii
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