English
Sets contained in some compact subset form a bornology on X; its cobounded filter is cocompact. See also relativelyCompact for closure-based bornology.
Русский
Множества, заключённые в некотором компактном подмножестве X, образуют борологию на X; их коподобный фильтр равен cocompact.
LaTeX
$$$ \\text{inCompact } X \\text{ на } X \\, \\wedge\\; \\operatorname{cobounded}_{(inCompact X)} = \\operatorname{cocompact}(X) \\, \\wedge\\; \\operatorname{le\\_cofinite}_{(inCompact X)} = \\operatorname{cocompact\\_le\\_cofinite}$$$
Lean4
/-- Sets that are contained in a compact set form a bornology. Its `cobounded` filter is
`Filter.cocompact`. See also `Bornology.relativelyCompact` the bornology of sets with compact
closure. -/
def inCompact : Bornology X where
cobounded := Filter.cocompact X
le_cofinite := Filter.cocompact_le_cofinite
