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Home  >  Transactions OF NAMP VOL1

13. Another Characterization of Local Completeness by Sunday Oluyemi Transactions of NAMP Vol. 1, (Nov., 2015), pp 91 – 98
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A separated locally convex space is locally complete if and only if every lower semicontinuous seminorm is bounded. 

Incidentally, we also establish 

(i) a seminorm analogue of [9, Definition 13-1-4 of the inductive limit topology], THEOREM 2.3, and 

(ii) the counterpart of [4, IMPORTANT CONSEQUENCE 5.7] for *(E,  E  ), THEOREM 3.9.

Keywords: locally complete, lower semicontinuous seminorm, bounded seminorm 2010 Amer.Math. Soc. Subject Classification 46A03, 46A08, 46A17, 46A20