Inverse limits and absolutes of 𝐻-closed spaces

Source abstract

The inverse limit of an inverse system of nonempty (respectively, minimal Hausdorff) H -closed spaces with continuous open surjective bonding maps is shown to be a nonempty H -closed (respectively, minimal Hausdorff) space. This result is used to resolve a conjecture, in the affirmative, of S. W. Willard: Every H -closed space is the continuous and open image of a minimal Hausdorff space.