A topological group G is sequentially h-complete if all the continuous homomorphic images of G are sequentially complete. In this paper we give necessary and sufficient conditions on a complete group for being compact, using the language of sequential h-completeness. In the process of obtaining such conditions, we establish a structure theorem for ω-precompact sequentially h-complete groups. As...

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...