Coincidence of the Dimensions of First Countable Spaces with a Countable Network

The coincidence of the \( \operatorname{Ind} \) and \(\dim\) dimensions for the first countable paracompact \(\sigma\) -spaces is proved. This gives a positive answer to A.V. Arkhangel’skii’s question of whether the dimensions \( \operatorname{ind} X\) , \( \operatorname{Ind} X\) , and \(\dim X\) are equal for the first countable spaces with a countable network.

DOI 10.1134/S1061920824030178