Formal Definition
In size theory, the size function associated with the size pair is defined in the following way. For every, is equal to the number of connected components of the set that contain at least one point at which the measuring function (a continuous function from a topological space to .) takes a value smaller than or equal to . The concept of size function can be easily extended to the case of a measuring function, where is endowed with the usual partial order . A survey about size functions (and size theory) can be found in .
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