Let $(X_s, \tau_s)$, for $s\in S$, be topological spaces such that $X_s\neq X_t$ for $s\neq t$; $s,t\in S$, and $X=\bigcup_{s\in S} X_s$.
We define topology $\tau$ in $X$ in the following way: $G\subset X$ is open iff $G\cap X_s \in \tau_s$ for each $s\in S$.
What sequences are convergent in $X$ ?