TOPOLOGIGAL VECTOR SPACE

Author (s) : DR.B.VENKATACHALAM

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Abstract :
In mathematics, a topological vector space (also called a linear topological space) 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, the latter thereby admitting a notion of continuity. More specifically, its topological space has a uniform topological structure, allowing a notion of uniform convergence.The elementsof topologicalvectorspacesaretypically functions or linear operators acting on topological vector spaces, and the topology is often defined so as to capture a particularnotion of convergence of sequences of functions. Hilbert spaces and Banach spaces are well-known examples.A metric linear space means a (real or complex) vector space together with a metric for which addition and scalar multiplication are continuous. By the Birkhoff-Kakutani theorem, it follows that there is an equivalent metric that is translation-invariant.

Keywords : Topological space, vector space

Conference Date : 17/09/2021

Pages : 106

Paper ID : IESMDT104