Continuity in Dreams?

Not sure if this technically counts as 'lucid', but here goes:

Does anyone have carryover from dreams? Or, like, do they ever go to a specific world where they, like, continue adventures and stuff? I'm fairly sure that I've done this, although I can't really remember right now.

One thing I do remember, is that I seem to be able to fly in most of my dreams. Although I'd call it levitation or hovering rather than flight. Basically, it uses the same rules as flight, but it takes a lot of effort to go fast and it takes a lot of effort to stop myself, both being problems due to the lack of friction involved. I have an outdoor version, which is more like flight, and an indoor version which is more weak, but more likely not to destroy everything, ha ha. I've had entire dreams that were just me figuring out the rules, what I can or can't do with it, etc.

I've noticed that in the dream, I can fly as long as I don't focus on it too much. I've had dreams where I'm blitzing across a city faster than traffic, until I start actively trying to use the flight, at which point I land and am stuck walking. That's not an every-time thing, though.

Anyway, I'm rambling. Anyone experience anything like this?

Well, I have my own world in dreams that has continuity.
People here call it persistent realms if I am not mistaken.

A good example of a continuous plot in dreams can be found in Hyu's DJ:
Lucid Dreaming - Dream Views - Hyu's Adventures - Dream Journals

When you say 'continue adventures and stuff', it reminds me of the dream-exit technique, where you choose to re-enter a dream after waking up. Maybe look into that. I don't know if this is relevant to your question though, as there is no real/long wake time involved here.

I would not say that it is a continuation of the same dream, just because you can fly in all of them. It may merely reflect your overall expectation to the physics and mechanics of your general dream-environment.