Topological Vector Spaces Free Download

Topological Vector Spaces

In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space (an algebraic structure) which is also a topological space, this implies that vector space operations are continuous functions. More specifically, its topological space has a uniform topological structure, allowing a notion of uniform convergence.The elements of topological vector spaces are typically functions or linear operators acting on topological vector spaces, and the topology is often defined so as to capture a particular notion of convergence of sequences of functions.Banach spaces, Hilbert spaces and Sobolev spaces are well-known examples.Unless stated otherwise, the underlying field of a topological vector space is assumed to be either the complex numbers C {\displaystyle \mathbb {C} } \mathbb{C} or the real numbers R . {\displaystyle \mathbb {R} .} {\displaystyle \mathbb {R} .}

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