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2016•The Journal of Nonlinear Sciences and ApplicationsOpen access

Some topological properties of fuzzy cone metric spaces

Tarkan Öner

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Abstract

We prove Baire's theorem for fuzzy cone metric spaces in the sense of Öner et al. [T. Öner, M. B. Kandemir, B. Tanay, J. Nonlinear Sci. Appl., 8 (2015), 610-616]. A necessary and sufficient condition for a fuzzy cone metric space to be precompact is given. We also show that every separable fuzzy cone metric space is second countable and that a subspace of a separable fuzzy cone metric space is separable.

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What this paper is about

We prove Baire's theorem for fuzzy cone metric spaces in the sense of Öner et al. [T. Öner, M. B. Kandemir, B. Tanay, J. Nonlinear Sci. Appl., 8 (2015), 610-616]. A necessary and sufficient condition for a fuzzy cone metric space to be precompact is given. We also show that every separable fuzzy cone metric space is second countable and that a subspace of a separable fuzzy cone metric space is separable.

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Available abstract

We prove Baire's theorem for fuzzy cone metric spaces in the sense of Öner et al. [T. Öner, M. B. Kandemir, B. Tanay, J. Nonlinear Sci. Appl., 8 (2015), 610-616]. A necessary and sufficient condition for a fuzzy cone metric space to be precompact is given. We also show that every separable fuzzy cone metric space is second countable and that a subspace of a separable fuzzy cone metric space is separable.

Key concepts: Mathematics, Cone (formal languages), Pure mathematics, Metric (unit), Metric space, Topological space, Topology (electrical circuits), Combinatorics

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