Cardinalities of some Lindelöf and ω1-Lindelöf T1/T2-spaces

We show that every first-countable countably paracompact Lindelöf T1-space has cardinality at most c; every first-countable ω1-Lindelöf Hausdorff space has cardinality at most 2c; every realcompact first-countable ω1-Lindelöf 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 Lindelöf number of every ω1-Lindelöf regular space of countable tightness is at most c.