A regular developable topological space $X$ with a nested development $\{F_{i}\}$ is called a Moore space, named after topologist R. L. Moore.

Moore spaces form a fertile bridge between point-set topology, metrizability theory, and Zermelo-Fraenkel set theory.

For example, Jones’ Theorem states that if $2^{{\aleph_{0}}}<2^{{\aleph_{1}}}$, then every separable normal Moore space is metrizable.