N-HIGH SUBMODULES AND h-TOPOLOGY

A submodule K of M is N-high if K is maximal with the property K ∩ N = 0. where N is a submodule of M. In this paper we study N-high submodules in the light of h-topopogy. In h-topology, Hk(M), k = 1,2,…,∞ form a neighbourhood system for zero. We characterize the submodules N of a h-reduced S2-model M for which all Nhigh submodules are bounded. We further characterize the submodule N of the same module M for which all h-pure N-high submodules are bounded.