from Wiktionary, Creative Commons Attribution/Share-Alike License
- adj. In which every open cover admits an open locally finite refinement.
One way to make this definition precise is through the technology of fine sheaves. says today, "[f] ine sheaves are usually only used over paracompact Hausdorff spaces".
Of course, may not be local, but it turns out that we can still prove Theorem 1 in this setting: A fine sheaf on a paracompact space has no cohomology.