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The way that I imagine 'curved space' is to take a rubber eraser - one of those large rectangular ones. The grab it and twist it. Hold the resulting shape in mind and now mentally remove the rubber. What you have left is the curved vacuum of a non-euclidean space time.

 

Or imagine a large box containing jelly. The jelly contains a regular rectilinear array of those sugar pearls. Take the box away so you just have the jelly. Squeeze it between your palms so that the blob of jelly is no longer rectangular. Finally take away the jelly and the twisted array of sugar pearls represents twisted space but only if you take away the sugar pearls as well leaving behind a vacuum which is curved spacetime.

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