Two applications of elementary submodels to partitions of topological spaces

We are looking at the sizes of partitions of topological spaces and show: No quasilin-delof space can be partitioned into more than 2140 sets Pi E P, where the character of P-i in X is countable and any two distinct P-i, P-j is an element of P can be separated by open sets with disjoint closure. No H-closed space can be partitioned into more than 2(N0) sets P-i is an element of P, where the character of P-i in X is countable and any two distinct P-i, P-j is an element of P can be separated by disjoint open sets.