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Home  >  Transactions of NAMP VOL.12

2. SOME SHORT NOTES ON THE TOPOLOGY OF THE SEMINORM by Sunday Oluyemi Volume 12, (July – Sept., 2020 Issue)
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SOME SHORT NOTES ON THE TOPOLOGY OF THE SEMINORM 

Sunday Oluyemi

Former ARMTI Quarters, Off Basin Road, Basin Area, Ilorin, Kwara State. 

Abstract

We prove that the topology of a seminorm is a vector topology, and then describe two local bases of neighbourhoods of zero, one from General Topology (GT) and another from Topological Vector Spaces (TVS). Some seminorm topologies’ equalities and inequalities are also established.  

Keywords: Topology, vector space, seminorm, topolo- gical vector spaces, neighbourhood of zero, local base of neighbour- hoods. 

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