π -Irreducible Mappings and K-Network of Infinite Compacts

In the paper the local density and the local weak density of topological spaces are investigated. It is proved that for a π-irreducible mapping f of a topological space X onto a topological space Y the followings hold: d(X) = d(Y ), wd(X) = wd(Y ), ld(X) ≤ ld(Y ), lwd(X) ≤ lwd(Y ). Moreover, it is showed that the functor of probability measures of nite supports Pn, the functor of the permutation degree and the functor expnpreserve the cardinality of k-networks of in nite compacts.