Nearly H-closed spaces

For a subset M of a topological space X, the θ-closure {ie626-01} M is defined as the set of all x X such that any closed neighborhood of x intersects M. A Urysohn space X is said to be U-closed if, whenever X {ξ} is a Urysohn space obtained from X by adding one point ξ, the point ξ is isolated in X {ξ}. The θ-closure operator is applied to study compactness-type properties of (weakly) U-and H-closed and closed-hereditarily U-and H-closed spaces. © 2008 Springer Science+Business Media, Inc.