I have posted [this question on MSE](https://math.stackexchange.com/q/4368193/223051) one year ago, but till now I did not received an answer. Therefore I have decided to post it here.

I have difficulty in understanding the meaning of "**A continuous family of symplectic forms**". I have seen this in many papers on symplectic geometry.

Does it mean, we have a one parameter family $\omega_t$, $t\in [a,b]$ of symplectic forms? If in that case why the word **continuity** though?<br>  Or does it mean we have a continuous map $f:[a,b]\to \Omega^2_\text{Symp}$, where $\Omega^2_\text{Symp}$ is the space of all symplectic forms on an ambient manifold? But in this case what is the topology of $\Omega^2_\text{Symp}$?

Can anyone please help clarify the definition for **continuous family**.

I have a strong sense that my second interpretation is the right one. But the thing is I don't know the topology of the space of differential forms $\Omega(M)$ on $M$. This might be a standard topology because I have seen in McDuff's book *Introduction to symplectic topology*, assumes that $\Omega^2(M)$ is a topological space.