**E. Ballico**

## Analytic Subsets of Products of Infinite-Dimensional

Projective Spaces

**abstract:**

Let $V_i$, $1\le i \le s$, be complex topological vector spaces with $V_1$
infinite-dimensional and

$Y$ a closed analytic subset of finite codimension of ${\bf {P}}(V_1)\times
\dots \times {\bf {P}}(V_s)$. Here we show that $Y$ is algebraic (at least if
each $V_i$ is a Banach space) and that any two points of $Y$ may be connected by
a chain of $s+3$ lines contained in $Y$.