/sci/ - Science & Math

>>15564413
If you have perps on both sides everything is a closed subspace by default, hence Cauchy sequences and the like are irrelevant.
You can't prove this by routing through [math]U \cap W \supseteq ( U ^ \perp + W ^ \perp ) ^ {\perp} \implies (U^\perp + W^\perp)^{\perp \perp} \supseteq (U \cap W)^\perp[/math], since that would let you prove that [math]U \supseteq U^{ \perp \perp }[/math], which isn't true for infinite-dimensional spaces, but I'm pretty sure it's still doable, even if it sucks and you have to expand everything to basic definitions.

>>15227047
Chain complexes or abelian categories.
>>15239434
I'm lurking but not posting because busy.
>>15239446
Correct.