A formal definition can be found at page 48 of "Kolmogorov, A. N., Fomin, S. V. (1970). Introductory Real Analysis, Translated and Edited by Richard A. Silverman"
But where is a separate procedure? I do not see the "separation" procedure in my imagination.
p.s. In my imagination, I have a bounded table R with too many needles that they enough to very-very near to touch all points in original set R. But it's only my imagination.