Oleksandr V. Maslyuchenko

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20242026

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math.GN2024

Compact subspaces of the space of separately continuous functions with the cross-uniform topology

Oleksandr Maslyuchenko, Vadym Myronyk, Roman Ivasiuk

We consider two natural topologies on the space $S (X \times Y, Z)$ of all separately continuous functions defined on the product of two topological spaces $X$ and $Y$ and ranged into…

math.FA2024

Takagi-van der Waerden functions in metric spaces and its Lipschitz derivatives

Oleksandr Maslyuchenko, Ziemowit Wójcicki

We introduce the Takagi--van der Waerden function with parameters $a > b > 0$ by setting $f_{a, b} (x) = n = 1 \sum \infty b^{n} d (x, S_{n})$ , where $S_{n}$ is a maximal $\frac…