= Summability domain of a regular matrix
{title2=$E_A=\{x\in\ell^\infty:Ax\in c\}$}
The summability domain is the inverse image of the <convergent sequence space> under the bounded matrix operator on the <l-infinity sequence space>. It is therefore a <closed linear subspace>. The <bounded divergence for every regular summability matrix> makes it proper, so it has empty interior and is a <nowhere dense set>. The <Baire category theorem> then ensures that countably many regular methods miss some common bounded sequence.
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