## A consistent example of a hereditarily -Lindelöf first countable space of size

István Juhász, Lajos Soukup and Zoltán Szentmiklóssy

Answering a question raised by Anishkievic and Arhangelski, we show that if then there is an -closed and partial order such that, in , there exists a 0-dimensional, , hereditarily -Lindelöf , and first countable space of cardinality . The question if there is such a space (even with hereditarily'' dropped) in ZFC remains open.

2000 Mathematics Subject Classification: 54A25, 54A35, 03E35

Key words and phrases: -Lindelöf, first countable, consistent example