On the question of the points of discontinuity of K_h C functions on continuous curves

Maslyuchenko Volodymyr Kyrylovych; Filipchuk Olga Igorivna

Maslyuchenko Volodymyr Kyrylovych ¹ , Filipchuk Olga Igorivna ²

¹ Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

² Department of Mathematical Problems of Management and Cybernetics, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: the points of discontinuity, continuous curves

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Abstract

Let X be a topological space, Y - a metric space, Z - a strongly σ" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"> $σ �$ -metrizable space. It is proved that the continuity points set of each KhC" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"> ${K h} �ℎ�$ -function f:X×Y→Z" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"> $f : X \times Y \to Z �:�\times�\to�$ is residual on continuous curves

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Cite

ACS Style: Maslyuchenko, V.K.; Filipchuk, O.I. On the question of the points of discontinuity of K_h C functions on continuous curves. Bukovinian Mathematical Journal. 2018, 1
AMA Style: Maslyuchenko VK, Filipchuk OI. On the question of the points of discontinuity of K_h C functions on continuous curves. Bukovinian Mathematical Journal. 2018; 1(314).
Chicago/Turabian Style: Volodymyr Kyrylovych Maslyuchenko, Olga Igorivna Filipchuk. 2018. "On the question of the points of discontinuity of K_h C functions on continuous curves". Bukovinian Mathematical Journal. 1 no. 314.

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