A topological space X is (1)
H(i), (2) H(ii), (3) R(i), (4) R(ii) if (1) Every open filter on X has nonvoid
adherence, (2) Every open filter on X with one-point adherence is convergent, (3)
Every regular filter on X has nonvoid adherence, (4) Every regular filter on X with
one point adherence is convergent. These properties, which were investigated by
Scarborough and Stone in a recent paper, arose naturally from the study of
minimal Hausdorff, H-closed, minimal regular and R-closed spaces. This paper
investigates similar properties for minimal Urysohn and Urysohn closed
spaces.
