LAUSR

We introduce the definition of h - perfect elements relative to a compactification $$h:M\longrightarrow L$$ h : M ⟶ L and show that if a collection of all such elements is a basis, then the remainder of a frame in this compactification is zero-dimensional. This concept yields what we call a full $$\pi $$ π -compact basis for rim-compact frames. Compactifications arising from full $$\pi $$ π -compact bases are investigated. We show that the Freudenthal compactification is the smallest perfect compactification and that its basis is full. Also, we exhibit the one-to-one correspondence between the set of all full $$\pi $$ π -compact bases and the set of all $$\pi $$ π -compactifications of a rim-compact frame L .