The'full'Gelfand Naimark theorem is a result for arbitrary ( abstract ) noncommutative C *-algebras " A ", which though not quite analogous to the Gelfand representation, does provide a concrete representation of " A " as an algebra of operators.
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For example, if a movie or a television series has been filmed in a town, the viewer is seeing a concrete representation of what the town actually looks like at street level; but if the town is merely mentioned in a single line of dialogue, the viewer hasn't learned anything except that the place exists.
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The original motivation of formal concept analysis was the concrete representation of complete lattices and their properties by means of " formal contexts ", data tables that represent binary relations between objects and attributes, thus tabulating pairs of the form " object " g " has attribute " m " . " In this theory, a formal concept is defined to be a pair ( " A ", " B " ), where " A " is a set of objects ( called the " extent " ) and " B " is a set of attributes ( the " intent " ) such that
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