This paper focuses on a distributed convex optimisation problem over networks with time-varying topologies. First, an event-triggered strategy is employed to reduce computation and communication load in the networked systems. Second, the exponential convergence of event-triggered zero-gradient-sum algorithm is guaranteed if the corresponding time-varying network topology satisfies a new connected condition, called cooperatively connected condition. This condition does not require topologies constantly connected or jointly connected but only requires the integral of the Laplacian matrix of the network topology over a period of time is connected. Hence, it is suitable for more general time-varying topologies. Third, a convergence analysis technique is developed which is based on the difference of the Lyapunov function rather than its differentiation. Finally, a simulation example is provided to verify the results obtained in this paper.