This is an axiomatic treatment of the properties of continuous
multivariable functions and related results from topology. The
author covers boundedness, extreme values, and uniform continuity
of functions, along with connections between continuity and
topological concepts such as connectedness and compactness. The
order of topics mimics the order of development in elementary
calculus, with analogies and generalizations from such familiar
ideas as the Pythagorean theorem.
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