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Functional analysis is the study of functions defined on certain abstract sets; these sets may vary greatly in their structure and the nature of their elements but they have in common the property that it is possible to define in them the notions of convergence, limit and so on: in other words, they are topological spaces. Most of the spaces studied in functional analysis have in addition algebraic properties: that is to say, addition and sometimes multiplication of their elements is possible.
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- Copyright © Mathematical Association 1959