The concrete objects of study in analysis are functions. One can often study functions in a useful way by thinking of them as elements of large sets of functions. These sets can be thought of as geometric spaces, and the functions in question are points of the spaces. Such spaces can be studied in their own right, without necessarily thinking of the points as functions, and results about such spaces can then be applied to concrete problems in analysis. The study of such spaces is called functional analysis; this is at the very least an instance of what is called abstract analysis.

The concrete objects of study in analysis are functions. One can often study functions in a useful way by thinking of them as elements of large sets of functions. These sets can be thought of as geometric spaces, and the functions in question are points of the spaces. Such spaces can be studied in their own right, without necessarily thinking of the points as functions, and results about such spaces can then be applied to concrete problems in analysis. The study of such spaces is called functional analysis; this is at the very least an instance of what is called abstract analysis.

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