Abstract
In this note we provide a new insight into trans-separable spaces, i.e. those which are separable by seminorms. This approach enables getting an easy proof of the fact that in a wide class of uniform spaces, containing $(DF)$ and $(LM)$-spaces, precompact subsets are metrizable.
Citation
S. Moll. L.M. Sánchez Ruiz. "Short proof of a metrization theorem." Bull. Belg. Math. Soc. Simon Stevin 14 (2) 317 - 320, June 2007. https://doi.org/10.36045/bbms/1179839223
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