The concept of physical and fractal dimension I. The projective dimensions

The projective dimensional analysis based on the projective extension of sc aling group and projective dimensional function is presented. We study the notion of self-similarity based on the physical quantities and not on topol ogy. The projective analog of the classical theorem-pi has been formulated in terms of (projective) numerical invariants. The additivity dimensions re placing fractal dimension are briefly discussed. Intuitive examples illustr ate presented ideas. (C) 2001 Elsevier Science Ltd. All rights reserved.