English
The product of bornologies on α and β gives a bornology on α×β with cobounded defined componentwise.
Русский
Произведение bornology на α и β задаёт bornology на α×β с ковобундированностью по компонентам.
LaTeX
$$$\text{Bornology on }\alpha\times\beta\;:\; \operatorname{cobounded}(\alpha \times \beta) = (\operatorname{cobounded}\alpha)\;\text{coprod}\; (\operatorname{cobounded}\beta)$$$
Lean4
instance instBornology : Bornology (α × β)
where
cobounded := (cobounded α).coprod (cobounded β)
le_cofinite := @coprod_cofinite α β ▸ coprod_mono ‹Bornology α›.le_cofinite ‹Bornology β›.le_cofinite