Small scattered topological invariants

We present a unified approach to define dimension functionslike $ rind$, $ rind_p$, $ rt$ and~$p$. We show how somesimilar facts on these functions can be proved similarly.Moreover, several new classes of infinite-dimensional spacesclose to the classes of countable-dimensional and$sigma$-hereditarily disconnected ones are introduced. Weprove a compactification theorem for these classes.