Topological Vector Spaces

Abstract

… every neighborhood of zero contains a balanced neighborhood of zero, … Let \(\mathcal{U}\) be a balanced neighborhood of θ in U and then \(E \subset t\mathcal{U}\) for some t. For \(\{u_{n}\} \subset E\), as α n → 0, there exists N such that if n > N, then \(t < \frac{1} {\vert \alpha _{n}…