Reducing heights of covers of topological spaces

Seminarium: 
Topologia
Osoba referująca: 
Adam Malinowski
Data spotkania seminaryjnego: 
poniedziałek, 21. Styczeń 2019 - 16:20
Sala: 
604
Opis: 
For a countable cover $\mathcal{A}$ of a compact (Hausdorff) space $Y$ with closed subsets we define its height, which is a measure of its complexity and generalizes the notion of the Cantor-Bendixson rank. If $X$ is another compact space and $f : X \to Y$ is continuous, the cover can be pulled back to $X$ and its height may drop, but can never increase. We inspect how much the height can be reduced as $Y$ and $\mathcal{A}$ are fixed while $X$ and $f$ vary.