36th Summer Topology Conference

July 18-22, 2022

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

"Uniformly dense subspaces in function spaces"

Aguilar, Joel

A set $A\subset C_p(X)$ is said to be uniformly dense if it is dense in the uniform topology. Since the uniform topology is finer than the topology of point-wise convergence, is expected that uniformly dense subspaces behave more nicely than arbitrary dense subspaces of $C_p(X)$. Indeed, there is a collection of properties $\mathcal{P}$ for which having a uniformly dense subspace with $\mathcal{P}$ also implies that $C_p(X)$ has $\mathcal{P}$; it turns out that the Lindelöf property is not one of this. In this talk I will present an example, obtained jointly with R. Rojas-Hernández, of a $\sigma$-compact space $X$ such that $C_p(X)$ has a uniformly dense Lindelöf subspace but $C_p(X)$ is not even normal.

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