Some critical remarks on the paper “A note on the metrizability of tvs-cone metric spaces” - Aleksić, Suzana M.; Paunović, Ljiljana R.; Radenović, Stojan N.; Vetro, Francesca (Vojnotehnički glasnik / Military Technical Courier, 2017)
This short and concise note provides a detailed exposition of the approach and results established by Shou Lin et al (Lin et al, 2015, pp.271-279). We show that the obtained results are not particularly surprising and new. Namely, using an old result due to K. Deimling it is indicated that tvs-cone metric spaces over solid cones are actually cone metric spaces over normal solid cones. Hence, there are only cone metric spaces over normal solid cones or over normal non-solid cones. One question still unanswered is whether an ordered topological vector space with a non-normal non-solid cone exists.
Keywords: tvs-cone metric space; metrizable; solid; normal; non-normal