I was just wondering whether there's some big difference between the topology generated by a seminorm and the norm it induces. For instance, Suppose $X$ is normed and $A$ is a subspace. $X/A$ is semi-normed, while if $A$ is closed, $X/A$ is normed. Do the quotients have very different topologies?
2026-03-28 01:48:48.1774662528
What's the difference between the topology defined by a seminorm and the topology defined by the norm it induces?
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