The Collins-Roscoe mechanism and D-spaces

We prove that if a space X is well ordered $(\alpha A)$, or linearly semi-stratifiable, or elastic then X is a D-space.

💡 Research Summary

The paper investigates the relationship between several generalized metric properties—specifically, well‑ordered (αA) spaces, linearly semi‑stratifiable spaces, and elastic spaces—and the notion of D‑spaces. A D‑space is defined via open neighbourhood assignments (ONAs): for every ONA N on a space X, there must exist a closed discrete subset D such that the family N