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

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