It has always been my impression that ‘Space’Time’ is discontinuous, or, to be more precise, that what we perceive is necessarily discontinuous — I am slowly coming round to the view that there may be an underlying reality which is, if you like, ‘continuous’, the perceived reality being a sort of froth on the surface of this deeper reality. Our Western scientific viewpoint, partly because of the influence of Newton and his ‘Theory of Fluxioms’, has always favoured continuity. But now some physicists are seriously re-considering the matter.
“We often speak of the fabric of space, as if it were continuous, but is it instead a kind of patchwork of jittering quantized bits?” writes Mariette DiChristina, the editor in chief of  Scientific American (in February 2012 issue).
The Director of Fermilab Particle Physics Centre, Craig Hogan, is planning an experiment which may “change what we currently think we know about the nature of space and time” (DiChristina).
“According to Hogan, in a bitlike world, space itself is quantum — it emerges from the discrete, quantized bits at the Planck scale (Note 1). (…) It does not sit still, a smooth backdrop to the cosmos. Instead, quantum fluctuations make space bristle and vibrate, shifting the world around with it. “Instead of the universe being this classical, transparent, crystaalline-type ether,” says Nicholas B. Suntzeff, an astronomer at Texas A&M University, “at a very, very small scale, there are these little foamlike fluctuations. It changes the texture of the universe tremendously.”  from “Is Space Digital?”  by Michael Moyer, (Scientific American, February 2012).

Notes :  (1)  The term ‘Planck scale’ can refer either to a space or time scale. Planck time is about 5.39 × 10 (exp –44) secs and Planck length is about 1.6 × 10 (exp –35) metres  (from Wikipedia)