| Autor: |
Maslyuchenko, Oleksandr, Myronyk, Vadym, Ivasiuk, Roman |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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 a topological or metric space $X$. These topologies are the cross-open topology and the cross-uniform topology. We show that these topologies coincides if $X$ and $Y$ are pseudocompacts and $Z$ is a metric space. We prove that a compact space $K$ embeds into $S(X\times Y,Z)$ for infinite compacts $X$, $Y$ and a metrizable space $Z\supseteq\mathbb{R}$ if and only if the weight of $K$ is less than the sharp cellularity of both spaces $X$ and $Y$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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