My apologies for this rather elementary question, but here goes: I didn't have any trouble figuring out how to prove that the 'standard' homotopy/isotopy definitions give rise to an equivalence relation, but I've been struggling trying doing the same for ambient isotopy.
I'll include the definition I'm using for good measure:
Two kots $K_1$ and $K_2$ are ambient isotopic iff there exists a continuous map $H: \mathbb{R}^3\times[0,1]\to\mathbb{R}^3: (x,t)\mapsto h_t(x)$ such that $H(x,0)=x$ for all $x\in \mathbb{R}^3$, $h_1(K_1)=K_2$ and every $h_t$ is a homeomorphism.
To prove that this is symmetric, my first instinct was to use the 'reverse time'-trick, but I don't see how that works because $H_1 \neq \operatorname{Id}$, right? The next thing I thought of was just taking the inverse function of every $h_t$, but I'm having trouble showing that $(x,t)\mapsto h_t^{-1}(x)$ is continuous.
I'd be happy if someone could provide me with a little guidance.