Show that Cantor set is a perfect set... | Filo
Show that Cantor set is a perfect set... | Filo
1 month ago
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Construct a two-dimensional Cantor set in the unit square {(x, y): 0 ≤x, y ≤1} as follows. Subdivide the square into nine equal parts and keep only the four closed corner squares, removing the remaining region (which forms a cross). Then repeat this process in a suitably scaled version for the remaining squares, ad infinitum. Show that the resulting set is perfect, has plane measure zero, and equals C ×C. | Numerade
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