Cardinalities of some Lindeloef and ω_1 -Lindeloef T_1/T_2-spaces

摘要

We show that every first-countable countably paracompact Lindeloef T_1 -space has cardinality at most c; every first-countable ω_1 -Lindeloef Hausdorff space has cardinality at most 2~c; every realcompact first-countable ω_1 -Lindeloef space has cardinality at most c. In all these results, first countability can be replaced by countable tightness plus either countable or countable closed pseudocharacter. We also show that the Lindeloef number of every ω_1-Lindeloef regular space of countable tightness is at most c.