# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Extension of mappings to non-Tychonoff spaces"

#### Reznichenko, Evgenii

Let $X$ and $Y$ be countably compact spaces, $Z$ be a space, and $f: X\times Y \to Z$ be a separately continuous mapping. If $Z$ is a Tychonoff space, then there is a compact extension $bX$ of $X$, such that the mapping $f$ extends to a separately continuous mapping $\hat f: bX\times Y \to \operatorname{\beta}Z$ , where ${\beta}Z$ is the Stone–Cech compactification of $Z$. The paper discusses under what conditions there exist extensions $bX$ and $bZ$ of the spaces $X$ and $Y$, respectively, such that the mapping $f$ extends to a separately continuous mapping $\hat f: bX\times Y \to bZ$. The application of the obtained results to the problem of continuity of operations in groups with topology is considered.

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