Why not buy a fire extinguisher? I've been a renter most my life, and I've never lived a place where the landlord supplied fire extinguishers, but they've also never complained about me supplying my own.
That's a good question. This might be some kind of a "fireplace delusion" [1] kind of a thing, I've never really even considered it. I've never seen anyone have a fire extinguisher in a flat here in Finland, that might also be one reason. I guess that wouldn't be the worst purchase to make but I'd still much rather try not to put myself in a situation where I'd need one :)
