Some topological properties of fuzzy cone metric spaces

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.