Weakening of continuity and calculated multiplicity of reflections

Safonova Olga Volodymyrivna

doi:https://doi.org/10.31861/bmj2018.03.127

Safonova Olga Volodymyrivna ^1,2

¹ Department of Higher Mathematics, State University of Telecommunications, Kyiv, 03110, Ukraine

² Department of Mathematical Analysis, Taras Shevchenko National University of Kyiv, Kyiv, 03127, Ukraine

DOI: https://doi.org/10.31861/bmj2018.03.127

Keywords: quasicontinuity, bijection, one-to-one correspondence point, local homeomorphism point, countable level of mapping, complete metric space, set of the second category

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Abstract

Weakening of continuity and mappings of countable multiplicity for a value set of the second

category in image are considered in the case of complete separable uncountable spaces. The exi-

stence of quasicontinuity for the inverse mapping is proved. It is shown that if a set of the first

category is excluded there exists a dence set of local homeomorphism points on the complement

of space

References

1.Masliuchenko V.K., Mykhailiuk V.V., Sobchuk O.V. (1995). Research on native continuous reflection. Materials of the International Mathematical Conference devoted to the memory of Hans Ghana. Chernivtsi, Ruta, 192-246.

2.Masliuchenko V.K. (1999). A series of continuous images of Kete's space. (Doctoral dissertation). Chernivtsi National University of Yuriy Fedkovych, Chernivtsi, Ukraine.

3.Mykhailiuk V.V. (2008). Coordinate method and the theory of continuous continuous images. (Doctoral dissertation). Chernivtsi National University of Yuriy Fedkovych, Chernivtsi, Ukraine.

4.Nesterenko V.V. (2015). Weakened continuity of the inverse image. Bukovinsky Mathematical Journal, 3 (1), 81-86.

5.Nesterenko V.V. (2016). Analogues of continuity: connections between natural and aggregate properties and the decomposition theorem. (Doctoral dissertation). Chernivtsi National University of Yuriy Fedkovych, Chernivtsi, Ukraine.

6.Luzin N.N. (1953). Lectures on analytic sets and their applications. Moscow: GITTL.

7.Aleksandrov P.S. (1978). The theory of functions of a real variable and the theory of topological spaces. Moscow: Science.

8.Trokhymchuk Yu.Yu. (2008). Differentiation, internal maps and analytical criteria. Kyiv: Institute of Mathematics of the National Academy of Sciences of Ukraine.

9.Gauld, D., Greenwood, S., Reilly, I. (1999). There are variations of continuity. Topology Atlas, Invited Contributions, 4 (1), 1-54.

10.Kuratovskyi K. (1966). Topology, (Volume 1). Moscow: World.

11.Safonova O.V. (2017). About an incredible B-dimensional image. Laboratory of the Institute of Mathematics of the National Academy of Sciences of Ukraine, 14 (1), 230-237.

12.Safonova O.V. (2018). On a pointwise discontinuous mapping with values in regular spaces. Bukovinsky Mathematical Journal, 6 (1-2), 97-103.

https://doi.org/10.31861/bmj2018.01.097

13.Noir, T. (1973) .Onsemi-continuousmappings. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fi siche, matematicheskie naturali, Serie 8, 54, 132-136.

14.Grande, Z., Natkaniec, T. (1991). There are quasicontinuous bijections. Acta Mathematica Universitatis Comenianae. New series, 60 (1), 31-34.

15.Trokhymchuk Yu.Yu. (2014). Count multiplicity and category. Statement of the National Academy of Sciences of Ukraine, (1), 33-36.

https://doi.org/10.15407/dopovidi2014.01.033

16.Khausdorf F. (2010). Theory of sets, (Edition 5). Moscow: LKI.

17.Gelbam, B., Olmstead, J. (1967). Counterexamples in the analysis. Moscow: World.

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Cite

ACS Style: Safonova, O.V. Weakening of continuity and calculated multiplicity of reflections. Bukovinian Mathematical Journal. 2019, 6 https://doi.org/https://doi.org/10.31861/bmj2018.03.127
AMA Style: Safonova OV. Weakening of continuity and calculated multiplicity of reflections. Bukovinian Mathematical Journal. 2019; 6(3-4). https://doi.org/https://doi.org/10.31861/bmj2018.03.127
Chicago/Turabian Style: Olga Volodymyrivna Safonova. 2019. "Weakening of continuity and calculated multiplicity of reflections". Bukovinian Mathematical Journal. 6 no. 3-4. https://doi.org/https://doi.org/10.31861/bmj2018.03.127

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