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Radiation in long term need huge protection so it is easy to dig a simple tunnel and live there.
When you grow, you can grow the cave, downwards if neccesary, and pump the material out. It takes a lot of time, but you can grow.
If you want to build a huge dome, you will need a huge effort and it would be useless until was completed.
Certainly, both approaches could be combined and it could be chosen depending on the resources.
For really small body with gravity near neglible, even rotated colonies deformed to compensate gravity, (like inverted cones) could be build.
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Perhaps with small bodies an outer atmosphere, maybe with a pressure of 5mb, could be physically contained? As karov has previously suggested, the outer "skin" could be used to focus sunlight towards the central body, increasing it's effective insolation, whilst the outer atmosphere would provide meteorite and radiation protection. I'm actually coming round to the idea of having the outer layer as a semi-intelligent foam system, that could allow spacecraft and debris to pass through and close up afterwards. Obviously, if such a system failed, it wouldn't result in the destruction of the colony, which is it's appeal to me...
Using the example of a 10km diameter object, say a Trojan asteroid... there would be an inner atmosphere extending 1-2km from the bodies surface, enclosed by a 5-10m thick layer of clear ice on top of (probably) a clear plastic layer. Above this would be a gel layer which would flow to ensure it remains smooth and transparent. Surrounding this to an "altitude" of 10km would be a 5mb atmosphere contained by an envelope which focuses light towards the body, giving it an effective insolation comparable to Mars. There you have it, a 10km wide terraformed asteroid...!
"I'm gonna die surrounded by the biggest idiots in the galaxy." - If this forum was a Mars Colony
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