Are there 3.5 dimensional objects ?
Well, this depends on the definition of dimension. This is clearly impossible if you take topological dimension.
But there are notions of dimension related to the measure, i.e. to length, area, volume, -dim volume such Hausdorff dimension or Minkowski-Bouligand dimension.
These dimensions were introduced to measure dimensions of fractal objects.
According to definition of Hausdorff dimension, dimension 3.5 can have a subset ⊂ℝ4 ⊂ ℝ4 whose 4 dim. volume is 0.0. It means if you can cover it with very small 4 dimensional balls such that the sum of their volumes ∑()∑ ( ) gets arbitrarily close to zero.
The idea is to make thus sum bigger taking powers of ()( ) with 0<<10 < < 1 (recall that powers less than 1 of small numbers are larger than they the numbers).
The least potentially possible ∑()∑ ( ) will remain 0 if is close to 1, but at some point it may jump to some positive number or to infinity. If this snapping point for is 0.5 then will have Hausdorff dimension 3.5 as desired.