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A mathematical definition of the concept of finite resolution is given. Its properties, such as invenibiliiy, and continuity are studied. Operators acting on objects under finite resolution are divided into two groups, vertical and nonvertical, depending on whether or not they are continuous with respect to approximation sequences. Applications in image processing, mathematical morphology, and fractal geometry are discussed.
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Jiří Fridrich (1996) studied this question.
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