On the metrizability of suprametric space

Abstract

The question of metrizability of suprametric space is answered positively. The observed metric coincides with a suprametric in a way that convergence and continuity are preserved between suprametric space and associated metric space along with the propery of a Cauchy sequence. Consequently, a suprametric space is complete if and only if associated metric space is complete. Fixed point theorems in suprametric space are obtained as a corollary of well-known fixed point results.

Keywords

• elementary
• operators
• compact operators
• orthogonality
• gateaux derivative
• primary 46g05, 46l05
• secondary 47a30, 47b47