The scale of homogeneity in the local Universe with the ALFALFA catalogue

We use the scaled counts in spherical caps N (< theta) and the fractal correlation dimension D-2(theta) procedures to search for a transition scale to homogeneity in the local universe as given by the ALFALFA catalogue (a sample of extragalactic HI line sources, in the redshift range 0 < z < 0.06). Our analyses, in the 2-dimensional sky projected data, show a transition to homogeneity at theta(H) = 16.49 degrees +/- 0.29 degrees, in remarkable accordance with the angular scale expected from simulations, a result that strengthens the validity of the cosmological principle in the local universe. We test the robustness of our results by analysing the data sample using three versions of the N (