@BrianM.Scott OK. We assume $B(x,\epsilon)\cap G$ is empty. This means that there are no numbers inside $(g,h)$ for $g=\sup\{g':g'<x-\epsilon\}$ and $h=\inf\{g:g>x+\epsilon\}$.
But before, I said that there were some $g,h\in G$ that worked.
So markov processes are defined on continuous spaces. Markov chains are the discrete counterpart. Markov chains have a continuous time version. But I can't find anything about continuous time Markov processes. Is there any reason why Markov processes can't be time-continuous?
