An Axiomatic Specification of Euclidean Analysis

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Abstract
This paper is an attempt to formalise the concept of cluster analysis by the rigorous specification of a general clustering model. The model is defined in terms of a real-valued function, called a clustering function, and the specification consists largely of defining the domain of the function and presenting properties which the function must possess. The properties are given in the form of axioms, and these axioms are intended to implement the notion of clustering. A sample function is given and shown to be a clustering function, thus verifying the consistency of the axioms.

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