**"Uniformly dense subspaces in function spaces"**
#### Aguilar, JoelA 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. |