Directed bases with net convergence

Abstract

The concept of a basis having a sequence of elements in a topological vector space is extended to a concept of a directed basis having a net of elements in a topological vector space. This article provides a generalization of the classical result which states that every basis in a complete metrizable topological vector space is a Schauder basis.

Keywords

• directed set
• net
• schauder basis
• topological vector space