The sets of elementary geometry have associated with them a dimension. Points have dimension 0. Curves have dimension 1. Surfaces have dimension 2. Solids have dimension 3. When we leave elementary geometry, there is the possibility of considering point sets not falling into any of these clear-cut groups. Mathematicians have defined a general notion of dimension to help out in the study of such sets. In fact, they have done it in several different ways; one way of defining dimension may be useful for one purpose but not for another purpose.
KeywordsTopological Dimension Open Cover Fractal Geometry Ultrametric Space Finite Open Cover
Unable to display preview. Download preview PDF.