On σ-weakly Hereditarily Closure-preserved Family And CC_ω-spaces

On σ-weakly hereditarily closure-preserved family and CCω- spacesIn this paper, we discussed σ-weakly hereditarily closure-preserved family and CCω spaces respectively.At the first part, we proved that S Sω1 is a space with a σ- weakly hereditarily closure-preserving к-network such that it does not have any σ-hereditarily closure-preserving к-network. We also discussed a series of properties of spaces with a σ-weakly hereditarily closure-preserved network or к- network.At the second part, we proved a series of properties of CCω spaces. Also we improved a theorem about the relationship between CCω spaces and M- spaces given by Pareek.