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I am writing a small report and trying to be mathematically accurate in my terminology- I am trying to describe an arbitrary volume of gas, but this volume must (1) not have any holes (or bubbles where the gas cannot go) in it, and (2) must be one single volume, so a gas molecule from any point can reach any other point without jumping.

Am I right in thinking the second condition is satisfied if the volume is "connected"?

What is the first condition described by?

It can be any shape, just no holes.

Thanks,

Mike

edit- Also I am considering a third condition, that (3)anystraight line passing through the volume only crosses two boundaries- for example a skewer through a donut can cross four times if you poke it through a line in the 'plane' of the donut. Is there a word for this? I think it may relate to the curvature of the edge surface, must be positive or zero everywhere?

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# Properties of a volume in 3D Euclidean space

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