What is the smallest Volume possible in three-dimensional space?

[Olias]

And what are the minimum locations needed for a Volume to exist?

[alexepascual]

Olias, I think this is still controversial, some people think there is a minimum volume, distance, area, time, etc. while others think space and time are probably continuous. (Penrose?)(String theorists?)
Those who believe in quantized space talk about the Planck distance as the shortest distance possible. I don't remember the exact number as a fraction of a meter for the Planck distance but it is very, very small. (you can look it up in google)
If you are interested in these topics, you may also do a Google search on "quantum loop gravity".
There are some recent popularizations which you can probably find at your local Barnes and Nobles. Look for authors like Greene and Smolin.
Good luck, and let us know what you found.
--Alex--

[Wave's_Hand_Particle]

And what are the minimum locations needed for a Volume to exist?

And what is the smallest bit of 2-Dimensional Space that can exist within an area that is Bounded by 3-Dimensions?

Actually does a 2-D space have to be Smaller than 3-D space?..does Quantizizing(sorry about spelling) of 3-D, actually reveal that 2-D must exist within a volume of 3-Dimensional Volume?

If one compactifies a Volume of 3-D space, then at a certain limit a 2-Dimensional Volume can encompass the 3-D volume, one can actually make the statement that a discrete 3-D can be surrounded by an infinite 2-D volume, I know that some Brane models are using a sort of Dimensional transposition, where embbeded Branes inter-mingle, but what if higher and lower branes collide, what is the outcome of such things..if at all they are possible.

[masudr]

If you believe that spacetime (this includes space and time) is quantised, then there are definite limits as to how far we can "zoom in" since after a certain point space and time will be playing with each other.

If you think spacetime is continuous as did Newton and Einstein, then you can go zooming in forever and forever and forever. For any two points with a small distance (or any two moments) there is another point (or moment) in between.