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Suppose that is a Fréchet space, is a regular method of summability and is a bounded sequence in . We prove that there exists a subsequence of such that: either (a) all the subsequences of are summable to a common limit with respect to ; or (b) no subsequence of is summable with respect to . This result generalizes the Erdös-Magidor theorem which refers to summability of bounded sequences in Banach spaces. We also show that two analogous results for some -locally convex spaces...
Let be a complete multipartite graph on with and being its binomial edge ideal. It is proved that the Castelnuovo-Mumford regularity is for any positive integer .
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