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AN INTRODUCTION TO DIMENSION THEORY AND FRACTAL GEOMETRY : FRACTAL DIMENSIONS AND MEASURES

“When we say that space has the dimensions three, what do we mean? If to divide a continuum C it suffices to consider as cuts a certain number of distinguishable points, we say that this continuum is of dimension one. If, on the contrary, to divide a continuum it suffices to use cuts which form one or several continua of dimension one, then we say that C is a continuum of dimension two. If cuts which form one or several continua of at most dimension two suffice, we say that C is a continuum of dimension three; and so on.”