Topological Vector Spaces

  title={Topological Vector Spaces},
  author={H. H. Schaefer},
  journal={American Mathematical Monthly},
This chapter presents the most basic results on topological vector spaces. With the exception of the last section, the scalar field over which vector spaces are defined can be an arbitrary, non-discrete valuated field K; K is endowed with the uniformity derived from its absolute value. The purpose of this generality is to clearly identify those properties of the commonly used real and complex number field that are essential for these basic results. Section 1 discusses the description of vector… Expand
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