In this paper, we procure the concepts of P -I-quotient mappings, P -I-cs-networks, P -I-cs′-networks and P -wcs′-networks, and prove some properties of P -I-quotient mappings and P -I-cs′networks, especially P -J-quotient mappings and P -J-cs-networks on an ideal J of N. With these notions, we obtain that if X is a P -J-F U space with a pointcountable P -J-cs′-network, then X is a meta-Lindelof space.