Locally connected hereditarily Lindelöf compacta (Q649603)

Filipov in 1969 under CH constructed a~connected first countable hereditarily Lindelöf compact space which is not metrizable. Nyikos in 1982 asked whether MA\({}+\neg\)CH implies that every locally connected hereditarily Lindelöf compact space is metrizable. This question is natural because Filipov used a~Luzin set in his construction and MA\({}+\neg\)CH implies that there are no Luzin sets. In the paper under review the author shows that Filipov's example works also with a~weak Luzin set and he proves that it is consistent with MA\({}+{}2^{\aleph_0}=\aleph_2\) that there is a~non-metrizable locally connected compact space which is both hereditarily separable and hereditarily Lindelöf.