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QUOTIENT SPACE IN N-NORMED SPACE AND ITS TOPOLOGY

Reza Fahrul Arifin

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Abstract

Given an n-normed space (X,||⋅,…,⋅||) with n≥2 and M_A=span \{A} subspace of X. We construct the quotient space X/M_A from the n-normed space equipped by some norm. The quotient space X/M_A turns out to be a normed space. Furthermore, there is a relationship in convergence of sequences between X and X/M_A. Keywords: n-Normed Space, Quotient Space, Convergence of Sequences.

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What this paper is about

Given an n-normed space (X,||⋅,…,⋅||) with n≥2 and M_A=span \{A} subspace of X. We construct the quotient space X/M_A from the n-normed space equipped by some norm. The quotient space X/M_A turns out to be a normed space. Furthermore, there is a relationship in convergence of sequences between X and X/M_A. Keywords: n-Normed Space, Quotient Space, Convergence of Sequences.

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Available abstract

Given an n-normed space (X,||⋅,…,⋅||) with n≥2 and M_A=span \{A} subspace of X. We construct the quotient space X/M_A from the n-normed space equipped by some norm. The quotient space X/M_A turns out to be a normed space. Furthermore, there is a relationship in convergence of sequences between X and X/M_A. Keywords: n-Normed Space, Quotient Space, Convergence of Sequences.

Key concepts: Quotient space (topology), Normed vector space, Mathematics, Quotient, Space (punctuation), Continuous functions on a compact Hausdorff space, Strictly convex space, Norm (philosophy)

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