Insertion of semi-continuous functions and sequences of sets (Q624222)

Characterisations of various topological properties, such as (monotone) countable paracompactness or metacompactness, perfect normality and stratifiability, are given in terms of the insertion of a continuous function between two semi-continuous functions or shrinking or expanding sequences of sets. It is pointed out that a purported characterisation of monotone countable paracompactness is in fact a characterisation of monotone countable metacompactness.