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2018, vol. 66, iss. 1, pp. 1-8
Some critical remarks on the paper “A note on the metrizability of tvs-cone metric spaces”
aUniversity of Kragujevac, Faculty of Science, Department of Mathematics and Informatics, Serbia
bUniversity of Priština - Kosovska Mitrovica, Faculty of Teacher Education, Prizren-Leposavić, Serbia
cUniversity of Belgrade, Faculty of Mechanical Engineering, Serbia
dUniversity of Palermo, Department of Energy, Information Engineering and Mathematical Models (DEIM), Palermo, Italy,,,
Methods of Functional and Harmonic Analysis and PDE with Singularities (MESTD - 174024)
Methods of Numerical and Nonlinear Analysis with Applications (MESTD - 174002)

Keywords: tvs-cone metric space; metrizable; solid; normal; non-normal
This short and concise note provides a detailed exposition of the approach and results established by (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.
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article language: English
document type: Original Scientific Paper
DOI: 10.5937/vojtehg66-15128
published in SCIndeks: 08/01/2018
peer review method: double-blind
Creative Commons License 4.0

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