  We define the LS-category cat_g by means of covers of a space by general
subsets, and show that this definition coincides with the classical
Lusternik-Schnirelmann category for compact metric ANR spaces. We apply this
result to give short dimension theoretic proofs of the Grossman-Whitehead
theorem and Dranishnikov's theorem. We compute cat_g for some fractal Peano
continua such as Menger spaces and Pontryagin surfaces.
