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

Author O. V. Maslyuchenko
„ерн≥вецький нац≥ональний ун≥верситет ≥мен≥ ё. ‘едьковича

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), є6, 740Ц747. (in Ukrainian)

2. O.V. Maslyuchenko, Construction of $\omega$-primitives: the strongly attaineble spaces, Mat. visnyk NTSh, 6 (2009), 155Ц178. (in Ukrainian)

3. O.V. Maslyuchenko, The oscillation of quasi-continuous functions on pairwise attainable spaces, Houston Journal of Mathematics, 35 (2009), є1, 113Ц130.

4. O.V. Maslyuchenko, The discontinuity point sets of quasi-continuous functions, Bul. Austral. Math. Soc., 75 (2007), є3, 373Ц379.

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

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