Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x1, . . . , xn] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi’s theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and impl...

Every locally complete inductive limit of sequentially complete locally convex spaces , which satisfies Retakh's condition (M) is regular, sequentially complete and sequentially retractive. A quasiconverse for this theorem and a criterion for sequential retractivity of inductive limits of webbed spaces are given.