Continuous Functions of Vector Variables

This text is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. In the context of normed vector spaces, the author covers boundedness, extreme values, and uniform continuity of functions, along with the connections between continuity and topological concepts such as connectedness and compactness. Suitable for a course in multivariable calculus aimed at advanced undergraduates preparing for graduate programs in pure mathematics. Required background includes a course in the theory of single-variable calculus and the elements of linear algebra.