The characterizations of Lindelf space in view of accumulation point

In view of complete accumulation point and 1 accumulation point, some characterizations of Lindel[AKo¨D]f space are given. The following are main theorems. Space X is Lindel[AKo¨D]f space if and only if any subset A of X with |A|ω_1 has a complete accumulation point; Space X is Lindel[AKo¨D]f space if and only if X is a meta-Lindel[AKo¨D]f space and any subset A of X with |A|=ω_1 has a1 accumulation point.