Continuous functions and minimal regularity (Q1058183)

Filterbases are used to characterize the \(T_ 3\) spaces all of whose \(T_ 3\) continuous images are minimal regular and the \(T_ 3\) spaces all of whose \(T_ 3\) continuous images are strongly minimal regular. Also a construction is given for a noncompact \(T_ 3\) space whose every \(T_ 3\) continuous image is strongly minimal regular; additionally this space has the property that there is a decreasing chain of nonempty, strongly minimal regular subspaces such that the intersection of these subspaces is empty.