Note on metrizability and $n$-dimensionality
Keiô Nagami · Proceedings of the Japan Academy Series A Mathematical Sciences · 1960
This note gives firstly some metrizability conditions which are trivial corollaries of J. Nagata's general metrization theorem (1).Our metrization theorem can be applied to criterions for n-dimension- ality of metric spaces with the aid of the concept 'cushioned refine- ments' obtained by E. Michael (2).One of the benefits of this interesting concept is to include both closed closure-preserving refine- ments and open star-refinements (cf.Remark 1.5).Thus our criterion for n-dimensionality provides us with more general form than [4, Theorem 7.2 and Theorem 7.5_ where closed closure-preserving refine- merits and open star-refinements are essentially used respectively.It