It is well known that any metric space is paracompact. As a generalization of metric spaces, cone metric spaces play very important role in fixed point theory, computer science, and some other research areas as well as in general topology. In this paper, a theorem which states that any cone metric space with a normal cone is paracompact is proved. © 2010 Elsevier Ltd. All rights reserved.
Sönmez, A. (2010). On paracompactness in cone metric spaces. Applied Mathematics Letters, 23(4), 494–497. https://doi.org/10.1016/j.aml.2009.12.011