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In mathematics, the support of a real-valued function is the subset of the function domain of elements that are not mapped to zero. If the domain of f {\displaystyle f} is a topological space , then the support of f {\displaystyle f} is instead defined as the smallest closed set containing all points not mapped to zero.
In mathematics, the support (sometimes topological support or spectrum) of a measure on a measurable topological space (, ()) is a precise notion of where in the space the measure "lives". It is defined to be the largest ( closed ) subset of X {\displaystyle X} for which every open neighbourhood of every point of the set has positive measure.
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
Support (mathematics), subset of the domain of a function where it is non-zero valued; Support (measure theory), a subset of a measurable space; Supporting hyperplane, sometimes referred to as support; Support of a module, a set of prime ideals in commutative algebra
Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. [127]
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The dictionary and thesaurus in Dictionary are in an XML format, but make use of precompiled binary index files to access the XML file directly. Therefore, the lexicon cannot easily be modified. However, the user can add new words to the macOS system-wide spell checker , which uses its own lexicon.
The support function is a convex function on . Any non-empty closed convex set A is uniquely determined by h A. Furthermore, the support function, as a function of the set A, is compatible with many natural geometric operations, like scaling, translation, rotation and Minkowski addition. Due to these properties, the support function is one of ...
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